English auxiliary verbs combine into more complex constructions according to wholly inflexible rules: the sequence is always
- the modal component first (if it is present), with the following verb in its infinitive form
- the perfect component next (if it is present), using the auxiliary HAVE, with the following verb in its past participle form
- the progressive component next (if it is present), using the auxiliary BE, with the following verb in its present participle form
- the passive component next (if it is present), using the auxiliary BE, with the following verb in its past participle form
- the lexical verb is always the last.
Each construction is thus marked with a specific auxiliary verb, HAVE or BE, and there is a ‘ripple’ effect: the form (present or past participle or infinitive) of each verb is determined by the preceding component.
Note that the English 'modal' verbs can/could, may/might, must, shall/should, will/would are defective: they occur only in finite forms and have no non-finite forms (infinitives and participles).
Since a modal verb cannot be cast in the appropriate non-finite form, it cannot act as complement of a prior modal verb or auxiliary: except when two modals are conjoined (You can and should tell him), you can have only one modal verb in a clause, and it must be the finite first verb.
You occasionally hear paired modals in dialect speech, but this is emphatically non-standard and is generally taken to mark the speaker as uneducated.
The work-around for situations which call for "dual modalities" is to employ a periphrasis for the second modal:
*You might could do it → okYou might be able to do it.
A periphrasis like be able to VERB or need to VERB or be obliged to VERB in effect "restarts" the verb chain: a complex construction with its first element cast in the 'infinitive' may follow the to:
If you had planned better you might have been able to have been working offsite when he arrived.
In this case, however, the first element in the new chain cannot be a modal, because modals cannot be cast in the infinitive.