'May' is a modal auxiliary. These verbs don't work in the same way as standard verbs.
Here's how to conjugate 'may':
Indicatif
Simple present
- I may conjugate
- you may conjugate
- he may conjugate
- she may conjugate
- it may conjugate
- we may conjugate
- you may conjugate
- they may conjugate
Present continuous
- I may be conjugating
- you may be conjugating
- he may be conjugating
- she may be conjugating
- it may be conjugating
- we may be conjugating
- you may be conjugating
- they may be conjugating
Past perfect
- I may have conjugated
- you may have conjugated
- he may have conjugated
- she may have conjugated
- it may have conjugated
- we may have conjugated
- you may have conjugated
- they may have conjugated
Perfect Continuous
- I may have been conjugating
- you may have been conjugating
- he may have been conjugating
- she may have been conjugating
- it may have been conjugating
- we may have been conjugating
- you may have been conjugating
- they may have been conjugating