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Concourse 2

Semi- and marginal modal auxiliary verbs

semi

There is a general, essentials guide to modality and a guide to central modal auxiliary verbs taken one by one on this site (both those links will open in new tabs).
This guide focuses only on semi-modal auxiliary verbs and what are called marginal modal auxiliary verbs (including the verb let).
In some analyses, marginal modal auxiliary verbs are also placed in the category of semi-modal auxiliary verbs but that leads to too much imprecision for our purposes.

In the following you will find reference to dynamic, deontic, alethic and epistemic modality.  If the terms are unfamiliar, you can safely ignore them but there is a link at the end to a guide to types of modality in which they are explained.
Very briefly, however:

  1. dynamic modality refers to the language user's perception of willingness or ability
  2. deontic modality refers to the user's perception of obligation or its lack
  3. epistemic modality refers to the language user's perception of the truth of a proposition
  4. alethic modality refers to the truths which are independent of the language users

Semi-modal auxiliary verbs

There is a certain amount of disagreement about what constitutes a semi-modal auxiliary verb.  For the purposes of this guide, we are considering verbs which can act both as modal auxiliary verbs and as 'ordinary' lexical or main verbs.
When they are modal auxiliary verbs, they follow the usual rules for central modal auxiliary verbs for forming questions and negatives and not using the -s / -es inflexion on the 3rd person.  They also do not occur reliably with other modal auxiliary verbs.
When these verbs operate as lexical or main verbs, they may co-occur with central modal auxiliary verbs just like other main or lexical verbs.
The four verbs which are most often defined as semi-modal auxiliary verbs are dare, need, have to and used to.  If you are here only to consider one of them or marginal modal auxiliary verbs and the verb let, use this menu:

 dare  |  need  |  have to  |  used to  |  marginal modal auxiliary verbs  |  let

dare

dare

Dare is an ancient word with connections to words pre-dating Old English.  It comes from a presumed Proto-Indo European root and occurs in Sanskrit, for example, as dadharsha.  It also has cognate forms in Old Norse, Old High German, Gothic, Old Persian, Ancient Greek etc.  In all these languages it had the meaning of to be bold.
An older English form had the irregular past tense durst which survived into the late 19th century but only occurs in some dialects today.
The verb still retains its meaning of have the courage to.
Consider these examples:

Modal auxiliary verb Lexical or main verb
  1. She daren't phone her mother
  2. She dared not phone her mother
  3. Dare she phone her mother?
  4. She wouldn't dare phone her mother
  5. I wonder if she dare phone her mother
  1. She doesn't dare (to) phone her mother
  2. She didn't dare (to) phone her mother
  3. Does she dare (to) phone her mother?
  4. She wouldn't dare (to) phone her mother
  5. I wonder if she dares (to) phone her mother

The contention here is that all these sentences are correct grammatically.  What conclusions can you draw?
Think for a little while and then click here.

To many, the modal forms of the verb sound slightly stilted and old fashioned and the non-modal, lexical forms are, in fact, more common as corpus research has shown.  The non-modal forms are also more common in American English.

In most cases, the verb expresses dynamic modality because it refers to ability and willingness rather than to obligation imposed or likelihood imagined.
Other forms of modality occur in the three common set phrases with dare

Set phrases

Imperatives

Unusually for a modal auxiliary verb, dare can be used in the imperative mood so we allow, for example:
    Go on, dare ask a question
    Please don't dare to ask
although this is a rare use of the verb.

Transitive uses

  1. There is a transitive use of dare to mean challenge in expressions such as
        I dare you to jump
        He dared me to do it
        Did he dare you to do it?
    etc.  In this use the verb is always a lexical or main verb, never modal so we do not allow:
        *I dare you go
        *She dared me ask
        *Dared he you to do it?
  2. Another, even rarer transitive use of the verb occurs in expressions such as:
        She dared the water
        I dared a question
    where the meaning is something like have the courage to try.
    Again, the verb is always lexical, never modal, in this meaning.

Here's a summary of this verb, which, as all summaries do, leaves out some detail:
dare

need

need

Need is the only semi-modal which fits into the notions of possibility, necessity etc. along with the central modal auxiliary verbs.
It does, however, have two non-modal, lexical uses.  Consider these examples:

Modal auxiliary verb Lexical or main verb 1 Lexical or main verb 2
deontic meaning deontic meaning requirement (non modal meaning)
  1. She needn't phone her mother
  2. Need she phone her mother?
  3. Needn't she phone her mother?
  1. She needs to phone her mother
  2. She doesn't need to phone her mother
  3. Does she need to phone her mother?
  4. Doesn't she need to phone her mother?
  1. I need a drink
  2. I don't need anything else
  3. Do you need anything?

What conclusions can you draw?
Think for a little while and then click here.

There is fruitful ground for confusion here, not least in the distinction between, for example:
    She needn't have phoned her mother (but did)
and
    She didn't need to phone her mother (so didn't).

A further source of confusion is that the verb is usually used to refer to obligation, i.e., deontic modality, but it can be used to refer to logical necessity, i.e., alethic modality, as in, for example:
    A rectangle needs to have four sides
    How many sides does a rectangle need to have?
and in this case, it is always formed as a lexical or main verb.  When the verb expresses a positive universal truth, it cannot be used as a modal auxiliary so we do not allow:
    *The answer need be 6
However, in the negative, both
    A rectangle doesn't need to have four equal sides like a square
and
    A rectangle needn't have four equal sides like a square
are possible.
The negative is frequently formed with can't, as in:
    A square can't have more than four sides
and this implies necessity rather than lack of obligation.
Questions can be formed in either way but the modal use is often very doubtful:
    Does the metal need to be heated to melt?
    ?Need the metal be heated to melt?

Again, to many, the modal form, especially the question, sounds formal and stilted and again, the form is rarer in American English.

face

need as a face-saving device

There are times when need, must and have to may be used interchangeably to express obligation or its lack but there are some important differences in nuance.
For example:
    You must buy a ticket
    You have to buy a ticket
    You need to buy a ticket
may be considered synonymous and, in many cases, they are.
All of these are examples of deontic modality and that is to do with obligation and duty.  So, for example,
    You have to fill in a form
or
    You must fill in a form
refer to the hearer’s duty and the obligation placed on him/her by or via the speaker.  It is sometimes used casually in spoken language to mean that this is not an obligation on you personally but a general truth.
However, in
    You need to fill in a form
The semi-modal need implies that it is a general rather than personal requirement, to do with the logical necessity of something being true.
This form is often used, for example, in the passive as:
    To be processed, the form needs to be submitted before the end of the month
which states a conditional necessity rather than a personal obligation.
The verb is often used by corporate bodies to reduce the directness of an obligation placed on customers so while:
    You must return your completed form by the end of the month
sounds rude and demanding,
    You need to return your completed form by the end of the month
sounds far less threatening although the meaning is identical.

The verb often implies some undesired consequence in the way that must and have to do not.  For example, choosing the formulation
    You need to be at the station by 6 (or you'll miss the train)
expresses the preference for avoiding the unwelcome consequence while
    You must be at the station by 6
expresses more direct obligation.

Face-saving for the hearer is often the motivation for selecting need over the more direct model verbs of obligation.  In, for example:
    Everyone needs to be in the office by 8 o'clock
no personal obligation is implied because this is simply company policy and not my imposition on you or anyone else.  It is more polite and distances the speaker from any sense of assumed authority.  If, on the other hand, I say:
    Everyone must be in the office by 8 o'clock
I am laying an obligation on each member of the group personally.
Compare, too, the use of need in, for example:
    The bank needs to have these figures tomorrow
with
    You have to / must give the bank the figures tomorrow
because the first saves the face of the hearer by not imposing authority on him/her.

Finally, we can ignore (if we wish) any statement using must or have to because we are independent operators.  So, for example:
    You have to come at 6 o’clock
is an obligation hearers can ignore if they choose and that might upset someone else, but
    You need to come at 6 o’clock
is probably not, because it implies that the hearers will miss something important if they don’t, not that someone else will be upset.

Here's a summary of this verb, which, as all summaries do, leaves out some detail:
need
There is an argument that both lexical forms of this verb are transitive but the first one requires a nominalised verb phrase rather than a noun-phrase object.

have to

have to

Elsewhere on this site, have to is considered as a modal auxiliary verb proper primarily because it acts for the true modal auxiliary verb must in other tenses (past and future) and as a straightforward alternative to must in other contexts.
However, it shares structural characteristics with the semi-modal auxiliary verbs such as need, dare and used to so it is considered here.

The verb signifies the same sorts of modality as must, too, so, for example it can show:

  1. deontic modality (duty and obligation)
        I'm sorry, I have to leave now
    which can be expressed as:
        I'm sorry I must leave now
  2. epistemic modality (likelihood)
        That has to be his sister.  They are so alike
    which can be expressed as:
        That must be his sister.  They are so alike
  3. alethic modality (necessity)
        A prime number has to be divisible only by 1 and itself
    which can be expressed as:
        A prime number must be divisible only by 1 and itself

However, unlike must, have to exhibits two kinds of structure: as a modal auxiliary verb and as a lexical or main verb:

Modal auxiliary verb Lexical or main verb
  1. She had to come early
  2. She hadn't to be late
  3. Had she to come early?
  1. She had to come early
  2. She didn't have to be late
  3. Did she have to come early?

Formally, this is the case although some consider that examples 2. and 3. are somewhat stilted and old fashioned.  Maybe so, but they do exist and they are used.

Functionally, however, there are issues, the most obvious of which concerns the fact that have to in the negative signifies a lack of obligation whereas must signifies a negative obligation.
Compare, for example:
    You mustn't start before 9
which signifies that starting before 9 is forbidden
with
    You don't have to start before 9
which signifies that starting before 9 is permitted but not required.
Both these forms refer to deontic modality, of course.
There is, in other words, a functional difference between sentences 2. and 5. above.
Sentence 2 suggest she had an obligation not to be late but sentence 5. suggests that she chose to be late and there was nothing to prevent her coming on time.

However, if the verb is used in its guise as a modal auxiliary (forming negatives and questions like central modal auxiliary verbs), the case is altered.  If we say, instead:
    You haven't to start before 9
we are effectively saying that it is forbidden to start before 9, not that it is permitted but not required, so it is functionally the same as
    You mustn't start before 9.

In interrogative sentences, the situation is simpler albeit inconsistent with the negative uses:
    Must I be here at 9?
or
    Mustn't I be here at 9?
    Do I have to be here at 9?
or
    Don't I have to be here at 9?
and
    Have I to be here at 9?
or
    Haven't I to be here at 9?
all suggest reference to obligation, not its lack, and it makes no difference whether the question form is positive or negative (so the 'rule' that the negative of have to always expresses a lack of obligation is not completely accurate).

bears

The relationship between have to and must

Because must is, as are all pure or central modal auxiliary verbs, defective, no inflected forms are available to signify tense and aspect and the verb cannot be used beyond the present tense.  We cannot have, therefore:
    *I musted go
    *I will must go
    *I am going to must go
    *I have musted go
    *I had musted go
    *I am musting go
and so on as is perfectly possible in a range of other languages.
Failing the forms, English makes do with have to as the auxiliary verb of choice and all forms are available:
    I had to go
    I will have to go
    I am going to have to go
    I have had to go
    I had had to go
    I am having to go
etc.

type

The types of obligation signified by have to

It is sometimes averred that have to applies to external obligation placed on a person and must is used for internal senses of obligation and duty.  It follows that:
    I have to write to my mother
is an obligation placed on me by another and
    I must write to my mother
is a sense of duty I am imposing on myself to commit to an action.
This is a very doubtful assertion and the forms in the present tense are used in free variation by many speakers with those from the USA, in particular, often preferring have to to must in all senses.
There are other problems with this assertion:

  1. It cannot apply to past and future forms because must is structurally unable to occur so:
        I had to write to my mother
    or
        I will have to write to my mother
    cannot be compared to some kind of internal obligation using must because no form with that verb is available.
  2. We saw above that have to (like must) can signify other forms of modality so, for example:
        He must be the bride's father
    cannot be contrasted with
        He has to be the bride's father
    because neither sentence denotes any kind of obligation, internal or otherwise.  The sense concerns the likelihood of a proposition being true and that is epistemic modality.
  3. By the same token:
        The answer must be between 0 and 1
    cannot be contrasted with
        The answer has to be between 0 and 1
    because, again, neither sentence refers to obligation at all but to a necessary truth.
  4. It is not always clear whether an obligation is internal or external so, for example:
        This tooth is getting worse and I must get to a dentist
    is as likely as:
        This tooth is getting worse and I have to get to a dentist

It is also suggested that must refers to a specific obligation and have to refers to more general obligations so, it is averred:
    I must tell her the truth
is correct and so is:
    We have to tell the truth at all times
but the alternative formulations:
    I have to tell her the truth
and
    We must tell the truth at all times
are somehow wrong.
That is nonsense, of course, and the same issues with other tenses intervene to show that.  The only way to express the past or future obligation is:
    I had to tell her the truth
    I will have to tell her the truth
and
    We had to tell the truth at all times
    We will have to tell the truth at all times
so, whether the obligation is general or specific cannot be a consideration.  The same applies to the insertion of progressive or perfect aspects.

Finally, it is also often suggested that we use must to refer to duties we impose on others and we reserve have to to imply that the obligation comes from elsewhere (a similar but slightly subtler idea than the external-internal distinction).  So, it would follow that we should prefer:
    You must be careful (because I require it)
to
    You have to be careful (because other authorities require it).
There is slightly more substantiation for this distinction and little doubt that some English speakers will prefer have to to signify a rule and must to signify a personal admonition so making a difference between:
    Must I wear a uniform?
to mean:
    Do you insist that I wear a uniform
and
    Do I have to wear a uniform
to mean
    Is there a rule about uniform wearing?
However, whether this distinction exists is slightly doubtful and whether it is worth troubling most learners with it is even more doubtful.  It is unlikely that most native speakers would wince if the modal auxiliary verbs were used in reverse.

?

Interrogatives

One distinction between the verbs does, however, have statistical substantiation: native speakers will usually opt for have to in question forms and the use of must is often seen as rather rare and formal.  So, for example:
    Do we have to follow the signs?
is, it seems, preferred to
    Must we follow the signs?
The even rarer form:
    Have we to follow the signs?
in which have to functions more nearly as a central modal auxiliary verb is now virtually extinct although the form with got in:
    Have we got to follow the signs?
is, in British English. still common.

bears

The relationship between have to and need

It is also suggested that have to is the form of choice to replace need in the past and future so, by this 'rule', we should prefer:
    I had to buy another ticket
over
    I needed to buy another ticket
and
    I will have to buy another ticket
over
    I will need to buy another ticket

This is another pseudo-rule.  It is the case that the somewhat formal use of need as a modal auxiliary verb as in, e.g.:
    Need I buy a ticket?
has no past or future form but that does not mean that we replace it with have to.  We can equally well use need as a lexical or main verb and choose to say:
    I need to buy a ticket
by inserting the to-infinitive instead of the bare infinitive.
The only time when the forms are clearly distinguishable is in the past when, as we saw above in the discussion of need, there is a difference between:
    I didn't need to call him (so I didn't)
and
    I needn't have called him (but I did)
and between
    I didn't have to call him (so I probably didn't but may have)
but that is not to do with the use of have to.

used to

used to and would

Commonly, the first of these two verbs id referred to as used to rather in the way that the central modal auxiliary verb is referred to as ought to.  It is arguably more logical and consistent to suggest that the verb is used and that it is followed grammatically by the to-infinitive.  (The same consideration applies to ought, incidentally.)

The verb is used to talk about

There used to be (!) two forms with identical meanings, thus:

Modal auxiliary verb Lexical or main verb
  1. She used to live in Margate
  2. Used she to live in Margate?
  3. She usedn't to live in Margate
  4. Usedn't she to live in Margate?
  1. She used to live in Margate
  2. Did she use(d) to live in Margate?
  3. She didn't use(d) to live in Margate
  4. Didn't she use(d) to live in Margate?

Notes:

  1. The modal forms are still encountered and should (perhaps) be taught for recognition purposes but the non-modal, lexical or main verb is now more common and, it seems fair to presume, will continue to grow in popularity.
    To many, the modal form is formal, stilted and even wrong.
  2. There is no requirement only to use the modal in non-assertive contexts.  This is unlike need and dare (see above).  So the verb maintains its form in questions, statements and negatives (sentences 1. to 4.).
  3. There is some spelling confusing.  The 'd' is optional where shown in brackets, compulsory otherwise.
  4. Confusion with the be/get used to structures, as in, e.g.:
        I'm used to working late
    can mostly be avoided if you don't present them in the same lesson.
  5. The pronunciation of this verb to express habit varies from the verb meaning employ: the 's' is pronounced /s/ in the former and /z/ in the latter.  Additionally, the 'd' is pronounced as /d/ in the main-verb use but as /t/ in the modal auxiliary use.  For example:
        I used a hammer (/ˈaɪ.ˈjuːzd.ə.ˈhæ.mə/)
    vs.
        I used to work hard (/ˈaɪ.ˈjuːstə.ˈwɜːk.hɑːd/)
    Many learners have trouble with this.

used to vs. would

Used to can be replaced by would usually after used to has set the scene.  For example:
    We used to take our holidays in Margate where we would stay in a guesthouse and would go swimming every day ... .
This is sometimes considered a time-frame function so used + to is used to set the overall time frame in which the events and actions are referred to with would.  Thus, in this example, We used to take our holidays in Margate serves to set the time frame in which all else takes place.
An allied point is that when the topic changes, used is again the verb which signals it.  So, for example, after the holiday anecdote we may encounter:
    After the holiday, when I got back to work I used to miss the freedom and would find it difficult to focus on the job.
This is called the episode boundary marking use of the verb and serves to mark the change.

It is often averred that only used to may refer to past states rather than actions:
    He used to be so slim
not
    *He would be so slim.
This is an often-used classroom rule but it is another pseudo rule, in fact.  There are exceptions to it when it comes to the use of copular verbs.
Would can be used with verbs which convey the relationship between subject and complement like be, appear, seem, remain etc. in, e.g.
    She would sometimes be a difficult person to talk to
    He would often appear uninterested
    I would remain in the house
Frequently, we insert time adverbials in these formulations.
The distinction here is to do with the adjective which is used:

  1. When we use an adjective which is stative or inherent to the subject and not under its control, the use of would is forbidden so, for example:
        *She would be short
        *They would be French
        *My mother would be beautiful
    etc. are all disallowed because the characteristic is not variable.
  2. However, when the adjective is dynamic or non-inherent in nature, would can be used to express the past state as in, for example:
        She would be obstructive
        They would be curious
        My mother would be happy

Another way of putting this is to distinguish between temporary, repeated or permanent states:

  1. Temporary or repeated states are allowed with would so we encounter:
        She would get irritable if I asked too many questions
        She would often be found in the garden
  2. Permanent states are not allowed with would so we do not encounter:
        *She would be an impatient person
    although
        She would get impatient
    is allowed because the state is temporary.

In the negative and interrogative forms would is often avoided in favour of used to because to many:
    I wouldn't get up early when I was on holiday
and
    Would you often have lunch on the terrace?
sound stilted.

Here's a summary of these verbs, which, as all summaries do, leaves out some detail:
used to and would

ambiguity

The anomalous nature of used and would

Modal auxiliary verbs (whether central of semi-) express the notions of truthfulness, likelihood, impossibility, duty, advice, obligation, willingness and so on.  Those terms are dismissed elsewhere on this site in favour of the concepts of epistemic, deontic, dynamic and alethic modality, incidentally.
However, it is quite arguable that both used and would in the meaning we are discussing here are, in fact, not modal in the true sense at all.  What both verbs are doing is signalling that a verb is to be considered both past and habitual in aspect.
If that is the case, a strong argument can be made that they are acting as primary rather than modal auxiliary verbs just as, e.g., have, be, do, get and will function to signal, perfect, progressive, causative, passive, future and other aspects of the verb.
For example, in:
    She has been running for the bus
we have the verb have acting to signal the perfect aspect and the verb be signalling, with the -ing participle, that the action is progressive.  That is what primary auxiliary verbs do.
By analogy, we should consider, therefore that used in:
    We used to visit my grandmother
and would in:
    We would visit my grandmother
are both signalling that the aspect of the verb is habitual and the tense is past.
They are, therefore, acting much more as primary rather than modal auxiliary verbs and should be described (and taught) that way.
However, most authorities persist in classifying the structure used + to-infinitive and would as a semi-modal verbs and that is what is done here.

half moon

Semi-auxiliaries or Marginal modal auxiliary verbs

Apart from pure and semi-modal auxiliary verbs, there is a class of multi-word verbs which are often referred to as semi-auxiliaries (and just as often dumped into the semi-modal category).  They are also called marginal modal auxiliary verbs because they are often lexical equivalents of true modal auxiliary verbs.
What you call them is of little consequence but their behaviour requires special treatment in the classroom because they, too, act like modal auxiliary verbs insofar as they:

They all, however, make questions and negatives as main verbs do and cannot be inverted for questions or negated without an auxiliary (do) in the present and past simple tense forms.
They also all, where it is appropriate, take a third-person, singular -s or -es inflexion as well as conventional past-tense markers and aspectual features.
However, many of these verbs cannot be used in progressive or continuous aspects.  Where this is the case below, it is noted.

A short list includes:

happen to
As in, e.g.,
    I happened to see John yesterday.
The sense is
    By chance I saw John
rather than by arrangement or plan.
The verb is not used in the progressive aspect.  So:
    *I was happening to speak to Mary
is not allowed.
The question form is allowable:
    Did she happen to meet him?
but the negative is questionable at best:
    ?She didn't happen to meet him
be (un)able to
This is sometimes described as a modal verb because it expresses dynamic modality in tenses or combinations of modalities that are forbidden to the defective central modal auxiliary verb can / could.  It is, in fact much simpler than that being a simple adjective linked to its subject by the copula be or by a pseudo-copula such as become, appear, end up, seem etc.
Because its function is always to refer to ability rather than permissibility or likelihood, it is more limited in its use than can / could.  For example:
    He was able to swim well as a child
    She might be unable to come at that time
    Were you able to see the doctor?
    I won't be able to help, I'm afraid
    She seemed able to move it
    He became unable to climb the stairs as he got older
etc.
Because the adjective is stative rather than dynamic, that is to say not under the direct control of the subject, progressive and imperative forms are not allowed so we do not encounter:
    *She was being able to do it
    *Please be able to come
etc.
The first difference with this form is that it can refer to a specific rather than a general ability so while both:
    He could swim well as a child
    He was able to swim well as a child
refer to the person's general ability
    He was able to swim across the river
refers only to a specific instance and
    He could swim across the river
can only refer to the generally demonstrated ability to do so, not any specific event.
Secondly, the past use of the be able to construction refers to a successful attempt in a way that the use of could have does not.  For example:
    I was able to talk to the boss
suggests a successful outcome but
    I could have talked to the boss
suggests that the speaker did not, in fact, do so.
care to
This is similar in sense to would like to but can only be used non-assertively, in questions and negatives, so we can have:
    Do you care to go out?
    I don't care to eat in smoky restaurants
but not
    *I care to eat out
The verb is not used in the progressive aspect.  So:
    *I wasn't caring to eat out so often
    *Are you caring for something to eat
are not allowed.
The verb is often combined with would in polite offers such as:
    Would you care for some more tea?
etc.
mean to
This semi-auxiliary is often used for current intentions in the same way that going to is used as in, e.g.,
    I mean to call on him on my way.
    I've been meaning to ask you about this
The verb can be used in this sense in all forms, positive, negative and interrogative:
    Does she mean to go to the shops?
    I don't mean to get the train
but there is some ambiguity because, e.g.:
    She didn't mean to be nasty
refers to her intention, not her plan whereas:
    I meant to go to the shops
implies a frustrated past plan akin to:
    I was going to go to the shops
but didn't for some reason.
(The verb mean followed by a -ing form is not in this category.  That verb signifies that something is involved or implied as in:
    I need a new car but that means spending money I don't have.)
seem to
This verb is often classified (wrongly) as always a copula.  It is a copular verb when it is used without another verb as in, for example:
    He seems happy
    She is seeming a bit down these days
The sense of seem to is different and is usually one of doubt or uncertainty so it belongs with the central modal auxiliaries such as might, may, could etc. as in, e.g.,
    He seems to be unhappy.
It expresses epistemic modality because it concerns the speaker's view of the likelihood of a proposition being true.  In this sense, seem to cannot be used in the progressive aspect so:
    *He is seeming to be unhappy
is not allowed.
Questions and negative uses are permitted.
tend to
In the present tense this verb suggests preference (and, therefore, habit) as in, e.g.,
    I tend only to watch the news on TV
    I am tending to eat less meat
In the past, however, it often performs the same function as the semi-modal used to as in, e.g.,
    We tended to take long walks on our holidays
compare:
    We used to take long walks on our holidays
or
    We would take long walks on our holidays.
Unlike used to and, obviously, would, tend to can be used in the progressive / continuous aspect so:
    We were tending to get up later and later
is possible to express a habit in formation which is a useful concept not available with the other ways of expressing past habit.  We hear, therefore:
    I am tending to play less golf these days
    I was tending to practise less and less because I was so busy
which is not expressible with used to or would.
turn out to
This is often not classified as a semi-auxiliary, and it is not one in something like:
    The weather turned out nice
    She is turning out to be a real asset to the company
where it is a copular phrasal verb, linking the subject and the epithet or non-finite clause and with a meaning akin to become.  We can replace it that way and get:
    The weather became nice
    She is becoming a real asset to the company
However, it has affinities with copular verbs and means something like ended up in expressions such as:
    He turned out to want even more money.
which cannot be rephrased with become.
It cannot, in this sense, be used with the progressive aspect so:
    *He was turning out to want even more money
is not allowed.
Questions and negative uses are permitted.
be about to
This semi-auxiliary is also often used as an equivalent to going to but emphasises the close proximity of the events in time.
Both are used in the past to refer to a frustrated plan.
Compare, e.g.,
    I was about to have dinner when you called
with
    I was going to have dinner when you called.
Both are used in the present to refer to a future based on current evidence or previous experience (and so are epistemic in sense).  E.g.
    Look at the weather.  It's about to rain / It's going to rain
or
    Don't argue any more; she's about to / going to lose her temper.
The verb is not used in the progressive aspect but can be used for inanimate subjects.  We allow:
    The house was about to collapse
but not
    *It was being about to collapse
be on the point of
works in a very similar way and has a similar meaning emphasising even more strongly the close proximity in time of the intended action.  It can also be used to refer to a frustrated plan.  Examples are:
    She was on the point of interrupting when the meeting closed
    They are on the point of leaving so hurry if you want to go with them
went to
This is a real oddity.  It can only be used to refer to the past existence of an intention which was not fulfilled and exists in no other tense.  It means roughly the same as be about to, however.  For example:
    I went to pick up the stone but realised it was too hot to touch
which does not carry the usual sense of movement towards which went normally signals.  It is a direct equivalent of:
    I was going to pick up the stone but realised it was too hot to touch
Unlike going to, however, this form can never be used with inanimate subjects because it signals a pre-formed intention so, while we allow:
    The car was going to crash
we do not allow:
    *The car went to crash.
The final oddity is that it cannot easily be used in questions and negatives so both:
    *Did he go to pick up the stone before he realised it was too hot to touch?
and
    *He didn't go to pick up the stone before her realised it was too hot to touch
are not allowed.
be likely to
This is modal in nature and clearly expresses a degree of probability so belongs with central or pure modal auxiliary verbs like may, could, will etc. and concerns epistemic modality.  Compare, e.g.,
    He's likely to be late
with
    He may well be late.
The construction is not used in the progressive aspect.
In this sense the marginal modal suggests a greater degree of possibility than may, could or might but not the greater certainty signalled by will.
be supposed to
This has affinities with modal auxiliaries such as should, ought to and must (in some senses) and refers to obligation (deontic modality) and to likelihood (epistemic modality).
Compare, for example,
    You aren't supposed to be in here
and
    You shouldn't be in here
which are both deontic in meaning, referring to obligation or duty, with
    The train ought to be here at 6
and
    The train is supposed to be here at 6.
which are both epistemic, referring to the speaker's perception of the truth of a proposition.
There is sometimes a sense with this construction that the event or state has not taken / will not take place although it should.  Compare, e.g.:
    He's supposed to be here already (but he isn't)
    He should be here already (and I think he is)
    I should go (and probably will)
    I'm supposed to go (but probably won't)
The verb is not used in the progressive aspect.
teach

Teaching semi-auxiliaries

If the teaching of modality starts (as it very arguably should) with meaning and speaker perception, then integrating the semi-auxiliaries into lessons focused on notions such as probability, permission, prohibition, futurity, intention and so on is quite straightforward.
Even better would be a focus on epistemic and deontic modality which most marginal modal auxiliary verbs carry.
The forms are easy enough to teach and the usefulness of the verbs is often overlooked, especially as some have no clear modal-verb equivalents but still refer to the speaker's perception of events and states.

lets

let

This verb is somewhat anomalous, quirky, even, and many analyses will not consider it a modal auxiliary verb of any type.  Here it follows the section on marginal modal auxiliary verbs but could just as easily be inserted after the semi-modal auxiliary verbs proper.  It shares some modal characteristics as well as functioning as a causative or main verb in, e.g.:
    I let him believe I was enjoying the meal (causative)
    Do they let dogs in here? (main, transitive verb)
etc.
There is a guide to the causative on this site, linked below in the list of related guides.

When it takes on its modal clothes, the verb is used to oblige, make suggestions and express willingness (deontic or dynamic modality) and it works like this:

Obligation / Permission Offer Suggestion
deontic modality dynamic modality cohortative meaning
  1. Let him help
  2. Did she let you help?
  3. Did they let you come in?
  4. She doesn't let me help
  5. The boss lets me go early
  1. Let me help you
  2. Will you let me do it?
  1. Let's go to Margate
  2. Let's not go to Margate
    or
  3. Don't let's go to Margate

In the functions of offering, permission and obligation, the verb has no modal characteristics (it has a past form [irregular and unchanged], takes a third-person -s and forms questions and negatives with the do operator).  The form is usually one of a simple imperative and can be softened with please etc.

The verb works as a modal auxiliary, however, insofar as it cannot appear without a main verb and implies suggestion, obligation and so on.  In this regard, it acts often as a cohortative expression, inviting cooperation rather than expressing obligation (9, 10 and 11, above).

(Incomplete) Summary

summary


Related guides
the essentials of modality a simpler guide in the initial training section
central modal auxiliary verbs taking each central modal auxiliary verb in turn and identifying its function
modality: tense and aspect which considers modal auxiliary verbs and perfect and progressive forms
multiple modalities for the guide to some of the ways these forms may be used to combine different sorts of modality
complex tenses which also considers complex tenses in relation to modality
teaching modality for some more ideas transferable to the analysis above
types of modality for more on types of modality such as epistemic and deontic modality
mood for a short guide to indicative, imperative and subjunctive moods in English
copular verbs and complements for a little more on how seem and turn out can be used
causative for the guide to ways to express making something happen rather than doing it
assertion and non-assertion for a little more on the differences between these ideas
suasion for more on hortation and optative meanings