May as a modal verb

Cheryl may be at home, or perhaps at work. possibility

Johnny, you may leave the table when you have finished your dinner. give permission

May I use your bathroom? request permission

Jack may be upset. I can't really tell if he is annoyed or tired. (Present)

Jack may have been upset. I couldn't really tell if he was annoyed or tired. (Past)

Jack may get upset if you don't tell him the truth. (Future)

Jack may not be upset. Perhaps he is tired. (Present)

Jack may not have been upset. Perhaps he was tired. (Past)

Jack may not get upset, even if you tell him the truth. (Future)

You may leave the table now that you're finished with your dinner.

You were allowed to leave the table after you finished your dinner.

You may leave the table when you finish your dinner.

You may not leave the table. You're not finished with your dinner yet.

You were not allowed to leave the table because you hadn't finished your dinner.

You may not leave the table until you are finished with your dinner.

May I borrow your eraser?

May I make a phone call?

Requests usually refer to the near future.