What is the past perfect tense of may?

Answer 1

past perfect is had + past participle.

eg had seen, had eaten, had washed.

Modal auxiliary verbs like may are not used with past perfect eg

may had seen, may had eaten.

May is used with present perfect to show past possibility eg

may have eaten, may have seen, may have washed.

Answer 2

The past perfect tense of "may" is "might have." For example: He might have arrived before you called.