In spoken English, a request for permission "May I ... " is generally answered with can, cannot, or can't OR with may or may not - even if the question was formed using may.
"Yes, you can." or "No, you cannot / can't!"
Which isn't a modal for ability? must / be able to / can\can't / could\couldn't
must
Which isn't a modal for permission? may / be allowed to / had better / can
had better
Which isn't a modal of prohibition? mustn't / can't / don't need to / not be permitted to / may not
don't need to
Which isn't a modal to show obligation? must / have to / should have / need to / have got to
should have
Which isn't a modal to show no obligation? couldn't / don't have to / needn't / haven't got to
couldn't
Which isn't a modal for advice? should / ought not to / can / had better / shouldn't
can
Which modal do we use for regrets about the past? would have / could have / should have / must have
should have
Which modal don't you use to make requests? will / would / may
may
Which modal don't you use for possibility? could / couldn't / might not / may
couldn't
Which modal don't we use for making general statements about the past? could / used to / would / couldn't / wouldn't
couldn't
Which modal don't we use for expectations? should / may / will / shouldn't
may
Which modal verb don't we use for certainty? can / must / can't
can
Which modal verb don't we use for prohibition in the past? wasn't allowed to / couldn't / shouldn't have / wasn't allowed to
shouldn't have
