Multiple modalities

One of the defining characteristics of central modal auxiliary verbs is that, in standard varieties of English, the verbs cannot co-occur. We do not, therefore, allow:
    *She can must do it
    *John could might allow it
    *The president can't may have the answer
and so on.
This means that when we use central modal verbs to express various types of modality we are confined, in standard varieties of English, to one form of modality at a time. So, for example, if we want to express a range of permissibility, from obligatory to forbidden (deontic modality), we can do so using modal auxiliary verbs and we can also express degrees of likelihood (epistemic modality) and willingness or ability (dynamic modality) in the same way. However, we cannot combine deontic, dynamic and epistemic modality through the use of central modal auxiliary verbs. We only allow, therefore, for example:

Deontic modality (degrees of permissibility)
    You must fill in this form
    She should get herself a new laptop
    You can't go yet
etc.
Epistemic modality (degrees of likelihood)
    That must be her brother
    She should be here soon if she caught the right train
    I may be a bit late tomorrow because I I'm going for a drink
etc.
Dynamic modality (degrees of willingness and ability)
    I can help with that
    She won't help
    He could speak French when he was a child
etc.

and, as we saw above, no combination of different sorts of modality can be achieved with any central modal auxiliary verbs. On this site, those verbs are identified as:
can | could | may | might | must | shall | should | will | would | ought
and we also included had better because it acts in a similar way.
In the guide to central modal auxiliary verbs (linked below), incidentally, the analysis identified nine other defining characteristics but they do not concern us here.

There is a fourth form of modality which refers to the inevitable truth of a proposition because of the way the universe works, alethic modality, but, because the reference is to a universal, context-independent truth, it is not combined with other forms of modality. We cannot allow, therefore,
*A rectangle could have to have four sides
because it makes no sense.

If the terms deontic, epistemic and dynamic modality are obscure to you, you could follow the general guide to types of modality, linked below. What is said above, however, is enough for the purposes of this guide.

We have been careful to note that we are talking about standard varieties of English in terms of the non-co-occurrence of central modal auxiliary verbs. In many dialects of the language, not least Southern USA usage, central modal auxiliary verbs often co-occur so we may encounter, for example:
He should ought to be here
and so on.

In very casual speech, too, it is often observable that speakers of English are searching for a way to combine modalities so it is not impossible to encounter something like:
Of course, if the boss demands it, I might must be there
but this is non-standard and unlikely to be encountered in writing or more careful speech.

Communicative need

There are times when we need to combine types of modality to make our point clear so it is possible that we want to express something like:
There is a possibility that he will want to have the ability to change the ticket
but we cannot express the thought using central modal auxiliary verbs because:
*He may will can change the ticket
is obviously not allowed.

This restriction does not apply universally across languages, in fact, and many do allow multiple uses of equivalent verbs in single clauses. For example, the forbidden
    *He must can come
in English, can be translated as:
    Han måste kunna komma (in Swedish)
    Er muss kommen können (in German)
    Il doit pouvoir venir (in French)
    Debe poder venir (in Spanish)
    Musí být schopen přijít (in Czech)
and so on and in all these cases there is a co-occurrence of modal auxiliary verbs.
Learners from language backgrounds that allow the co-occurrence of modal auxiliary verbs may be confused and frustrated by the irregular nature of what is and is not allowed in English. That, of course, is a source of error because the temptation will often be to translate directly.

The workarounds

All human languages are capable of expressing all human thoughts so it is not surprising that English can express combinations of types of modality perfectly adequately.
How it does that is a confusing mishmash of forms, however, and the root of much difficulty for learners at all levels.

Combination 1: epistemic and deontic

We can combine expressions of likelihood and permissibility in these ways, the first two of which are the generally preferred routes and should be taught first. English happens to have a non-defective form for obligation (have to, don't have to, haven't to) so the following are possibilities:

Central modal auxiliary verb plus semi- or marginal-modal auxiliary verb
For example:
    John might be let go
    I may be needed to work tonight
    I might be supposed to do the work
    It may need to be done
    They might have to get a new one
    She could have had to take a bus
Central modal auxiliary verb plus a lexical or main verb
For example:
    John must be forced to do it
    They might be told to come
    They could be allowed to leave early
    I doubt she may be allowed in
Central modal auxiliary verb plus modal noun
    That could be an obligation
    She might have that duty
    It's a possibility I must be there
Central modal auxiliary verb plus a modal adverb or adjective
For example:
    It's inevitable she must earn more
    It might be compulsory
    That could be permissible
    That might be obligatorily done

Combination 2: epistemic and dynamic

English also happens to have a simple modal adjective form connected to its subject by the copula or a pseudo-copula: able to, become unable to etc. The combination is also describable as a marginal modal form and is so identified in the guide to semi- and marginal modal auxiliary verbs. It is often used to combine the types of modality like this:

Central modal auxiliary verb plus semi- or marginal-modal auxiliary verb
For example:
    John should be able to do it in time
    I may be unable to help tonight
    I might not be able to understand him
    They might not have been able to get a seat
An alternative analysis here is that the structure is simpler: a modal auxiliary verb plus a copular verb and a predicative adjective, able / unable.
Central modal auxiliary verb plus a lexical or main verb
For example:
    John might succeed in doing that
    That may work well
    They could manage the issue
    I can imagine that she intended to go
Central modal auxiliary verb plus modal noun
    That could be a success
    She may have had some ability
    It's a certainty that Mary can help
    She might have shown some willingness
Central modal auxiliary verb plus a modal adverb or adjective
For example:
    She must be capable of doing the work this week
    It might be doable
    That could be possible
    John could be willing to see her
    That might be successfully done

Combination 3: deontic and dynamic

It is here that a good deal of ambiguity arises in English because the modal auxiliary verbs used to express deontic modality (permissibility) and epistemic modality (likelihood) are often the same so, for example:
    I could have left my keys with John
means either:
    I might have left my keys with John (epistemic modality referring to a possibility)
or
    I was allowed to leave my keys with John (deontic modality referring to permission)
The combinations are possible, of course, but we need some co-text and context to disambiguate the forms.

Central modal auxiliary verb plus semi- or marginal-modal auxiliary verb (or the adjective (un)able)
For example:
    John should be able to do it in time
    Mary should be willing to help
    They must be able to help tonight
    I had better be able to explain it
    They won't have been able to get one
Central modal auxiliary verb plus a lexical or main verb
For example:
    John must get it done
    She must succeed
    They ought to manage the issue
    I can't do it again
Central modal auxiliary verb plus modal noun
    She should have some success
    She ought to have had more ability
    It's a certainty that Mary can help
    She may show some willingness
Central modal auxiliary verb plus a modal adverb or adjective
For example:
    She must be capable of doing the work this week
    It must be doable
    That could have been possible
    John should be able to do it
    That ought to be carefully done

Semi-modal auxiliary verbs

We see above that semi-modal auxiliary forms are frequently combined with other semi- and central modal auxiliary verbs to make meanings which combine two types of modality. On this site, semi-modal auxiliary verbs are identified as dare, need, have (to) and used (to). To that list, for our purposes here, we can add be able (to) because it, too, can function in multiple modal utterances.

These semi-modal verbs are often used to combine modalities as in, e.g.:

She might not dare to ask
combining epistemic with dynamic modality
I used to be able to speak Italian
combining dynamic modality with past habit
They used to have to get the water from a well
combining deontic modality with past habit
She has to be able to help
combining deontic and dynamic modality
We didn't used to need to get a permit
combining past habit with deontic modality

Marginal modal auxiliary verbs

There are a few marginal verbs which can combine with other forms to produce multiple modal meanings. Examples include:

He is supposed to be able to understand this program
combining deontic with dynamic modality
Will she care to come with us?
combining two forms of dynamic modality
She seems to be able to do this
combining epistemic and dynamic modality
I'm likely to have to take some medicine
combining epistemic and deontic modality

Summary of the patterns

Here's a summary with a single example of each type of construction. It is straightforward to use them as models to invent more examples.

summary

Teaching multiple modalities

Combining types of modality is, as we see above, not a simple matter in English and we also noted above that other languages are far more forgiving than English in this respect. The fact that English does not permit the co-occurrence of a range of central and other modal auxiliary verbs causes some difficulty because learners from many language backgrounds can see no logical reason why:
*He had to could be there
is not allowed.
This is, therefore, not an area with which we need to trouble lower-level learners but it is one which needs tackling at higher levels where more sophistication is needed.

Comprehension is always a good beginning in this area because learners may not notice that some sentences contain multiple modal meanings unless their attention is explicitly drawn to the phenomena. Here's one way of doing that:

Draw lines to connect the meanings on the left with the meanings on the right.
She must She can		She ought to be willing to help
She should She will		They may be able to help
I will I should		She has to be able to help
They may The can		I should be willing to help

and so on.

We can start from more simple forms and work our way up. For example:

In English, the forms of the left are all wrong (but they may be possible in your language). How can you rephrase them in correct English and keep the same sense? The first one is an example.
He must can leave soon	He must be able to leave soon
She should can go
They may can't do it
The had to could help

and so on.

When we get really sophisticated, we can begin to introduce some of the less common and more formal ways to combine modality using other, non-modal auxiliary verbs. As in, e.g.:

Rephrase the sentences on the left using modal auxiliary verbs where possible. The first one is an example.
She is obliged to learn to do this	She must become able to do this
It is possible they might be allowed to go home
It is unlikely she has the strength to lift it
It is probable that he is obliged to be late

Now try doing this the other way around.

Rephrase the sentences on the left using modal nouns, adjectives and adverbs but not modal auxiliary verbs. The first one is an example.
She must become able to do this	She is obliged to learn to do this
We might be able to ask questions at the end
They can't have to leave yet, can they?
She used to have to be at work at seven

and so on.

Communicatively, the area is more challenging but some kind of simulated communicative events can be set up for freer practice such as, e.g.:

Decide together on the abilities that someone applying for a job as a sales assistant / computer game designer / gardener etc. needs and discuss them with another pair to see if you have the same ideas.
Start from:
This person will have to be able to ...
Think about three obligations that lie in the future for you. Tell your partner(s) about them.
Start from:
By the end of this year / term / decade / century etc., I might have to be able to ...
My mother is 95 years old. Think about the things she was able to do once that she can't do now and see if you have the same list as another pair.
Start with:
Her mother used to be able to ...
All schools have rules. What were the rules in your school? Tell your partner about them.
Start with:
When we were at school, we used to have to ... and we weren't allowed to ... but we didn't have to ...

Many other scenarios are possible of course.

Related guides
central modal auxiliary verbs	for the guide to these non-co-occurring verbs
semi-modal auxiliary verbs	in guide which also considers marginal modal auxiliary verbs such as seem, tend, be about to etc.
types of modality	for the guide to types of modality such as epistemic and deontic modality
modal auxiliary verbs: tense and aspect	a guide which considers the modal auxiliary verbs in relation to perfect and progressive forms
complex tenses	a guide which considers complex tenses in relation to modality (I shouldn't have done it etc.)
teaching modality	for some ideas
the modality index	for links to a range of related guides