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Is it correct if somebody uses "can have had" instead of "may have had"?

  • I can have called him yesterday, but I don't remember speaking to him.
  • She can have done it but without proof we can't say for sure.

Does changing it from Past Perfect to Pluperfect change the meaning?

  • I could have called him yesterday, but I don't remember speaking to him.
  • She could have done it but without proof we can't say for sure.

Do "would" and "should" of the "Pluperfect" have similar in "Past Perfect"? While may (Past perfect) = might (Pluperfect) and can (Past perfect) = could (Pluperfect), what do would (Pluperfect) and should (Pluperfect) equal?

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I can't do that today

I couldn't do that when I was a kid

Here the tenses are different, repsectively present and simple past. However Pluperfect = Past Perfect

can't have done and couldn't have done are both in the same tense but the modals are different.

You are asking about the epistemic modality, that is the degree of confidence.

Increasing order of uncertainty

He must have done that / He may have done that / He might have done that

can have done is not grammatical, you should use must have done instead. However in a negative sentence it is fine:

He can't have done that / He may not have done that / He might not have done that

The difference between can't have done and couldn't have done is that the latter is about something we are sure of, whereas the former is about ability/possiblilty of an event that didn't happen.

Compare

She might have used the car

That's uncertain, I don't know if she did

She could have used the car

It was possible for her to use the car, but she didn't

Note: In some cases people use could have to mean may have/might have with could have

Lastly Should and Would don't have other forms

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