Stephen Buck wants to explain to a non-native English speaker why the following question is not possible in standard English:
May you do this for me?”
The modal verb may has many uses. The OED entry gives 26 numbered definitions with numerous sub-sections. One of the definitions is this one:
may: Expressing permission or sanction: be allowed (to do something) by authority, law, rule, morality, reason, etc. Now somewhat rare exc. (Brit.) in asking and granting permission
In standard English, when may implies permission, it is used in the asking or granting of it:
May I use the car tonight?
I may not have a Facebook account; my parents have forbidden it.
You may go to the zoo with us.
While it is possible to use may to ask for permission or to grant permission, we use will or can when we want to ask someone to do something for us:
May I use your telephone?
You may stay out until 10 p.m.
Will you do this for me?
Can you do this for me?
We use will when we know that what we’re asking is within the power of the person being asked:
Will you hold the door while I unload?
We use can when there is some doubt that the person is able/has permission to do what is asked:
Can you authorize this payment?
Can you help me move this piano?