Don't forget that "may" should be used for permission and "can" for ability. So it should be "May I interrupt?" because you clearly can (you are interrputing already), and it's "Can you eat all that?" because the question is whether you are capable of stuffing your face so much. However, in real world you will hear people say "Can I use your bathroom?" even though it's a question of permission and not your bladder function.

will - 100% may - ~50% might - ~30% can - first form (present simple) could - second form (past simple/subjunctive verb mood [=unreal/hypothetical])

if something is not sure,then I use may. can---I can do something.