Contracted forms

Unlike be and have (but not do), modals in the affirmative do not have contracted forms, except for will and would [I'll, I'd > 9.35, 14.17n3]. In speech, can, could and shall are 'contracted' by means of unemphatic pronunciation:

/, (etc.) can /kən/, /, (etc.) could /kəd/, I/We shall /ʃəl/

One modal at a time

Only one modal can be used in a single verb phrase:

We may call the doctor but not may and must together.

We must call the doctor

If we wish to combine the two ideas in the above sentences, we have to find a suitable paraphrase:

It may be necessary (for us) to call a doctor By comparison, we can use e.g. be and have together:

It has been necessary to call a doctor

Form of modal auxiliaries compared with future tenses

Each of the modals fits into the four patterns for future tense forms:

simple future [> 9.35]
future progressive [> 9.40]
future perfect simple [> 9.42]
future perfect progressive [> 9.42]
active passive

/ may see I may be seen

/ may be seeing - [but > 12.3n.6]

/ may have seen I may have been seen

modal + have been + present participle: / may have been seeing