[Modal auxiliaries] Polite Requests with I as the Subject (may, might, can and could)

used frequently	formal and polite
Rearely	High	Might I borrow your pen?
		May I borrow your pen (please)?
		Could I (please) borrow your pen?	Could has a present or future meaning, not a past meaning.
More	Low	Can I borrow your pen?

Typical responses

Certainly. Yes, centainly.	formal
Of course. yes, of course.	formal
Sure	informal