Which ones are correct:
May/can we go to the game?
May/can you do this for me?
can/may you come?
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"May" is asking permission so it needs to about yourself or a third party: "May I" or "May we" or "May my dog"
Can is a lot more flexible, can be a request of someone, asking about feasibility and/or asking permission, and would work in all cases.
So, "May/can we go to the game?" both work. "May" is more formal and little old fashioned.
"Can" works for all. "May" wouldn't work for the other two.
("May you" only works when permission is being asked of an unmentioned magical/mystical third-party - God/providence/etc - so "May you rest in peace", "May you rot in hell", etc. The Magical May apparently)