How to use causative verbs with modal verbs?

Though there are a number of online articles explaining the causative structure, I couldn't find anything related to causative model model verbs. Therefore, I would be delighted if someone could let me know which of the following sentences are correct in terms of grammar.

I would have / let / make my sister do something. (to talk about future situation)

I could have / let / make my sister do something. (to talk about a future or past situation)

I could have had / let / made my sister do something. (to talk about a past situation)

I might have / let / make my sister do it, it you need. (to talk about the future)

I might have had / let / made my sister do it, if you had requested. (to talk about the future)

Edit: changed 'model' to 'modal' in header. CJ