てもらってもいいですかcould you…?; would you mind…?
A request in the shape of asking permission. It looks like "may I…?", but もらって is in it, so the other person does it: "could you…?".
polite
Excuse me, could you take a photo for me?
to a friend
Could you hold this for a second?
How to form it
Verb in the て-form + もらってもいいですか
撮る → 撮ってもらってもいいですか. The も often drops: 撮ってもらっていいですか.
With friends
Verb in the て-form + もらっていい？
To someone above you
Verb in the て-form + いただいてもよろしいですか
Who does it?
てもいいですか asks whether you may do something. With もらって in the middle, you ask whether you may have it done for you. The verb in front is what the other person does.
May I open the window?
You open it. You are asking permission.
Could you open the window?
They open it. You are asking a favor.
How it sounds
Word for word it is "is it all right if I have you…?", so it comes out soft and a little roundabout. People say it every day: in shops, at work, to a stranger.
Sorry, could you say that again?
to shop staff
Could you show me that watch?
Excuse me, could I borrow a pen?
Yes, go ahead.
English turns it around: "could I borrow". The verb is still theirs: 貸す, to lend.
With friends, and to someone above you
With friends it is てもらっていい？. To a teacher, a boss or a customer, いただく takes the place of もらう, and いい often becomes よろしい.
to a friend
Sorry, could you wait a second?
to a teacher
Would you mind looking over this essay for me?
Close neighbours
てもらえますかN4
"Can I have you…?" A little more direct, and said to the same people.
Excuse me, could you take a photo for me?
てもらえない？N4
The same kind of question between friends, with no いい.
Could you take me to the station tomorrow morning?
The careful way to ask a favor of a teacher, a boss or a stranger.
Excuse me, could you tell me the way to the station?
Check yourself
1A colleague says this to you. Who turns the light off?
すみません、
Choose an answer to see why.
2You would like your boss to check an email you wrote. Which one fits?
Choose an answer to see why.
More detail
撮らせてもらってもいいですか
With a causative in front (撮らせて, "let me take"), it turns around again: you do it, with their leave, a soft "may I?".
Would it be all right if I took a photo here?
More sentences
Could you give me a hand for a moment?
Could you tell me how to read this kanji?
to a friend
Sorry, could you say that one more time?
staff to a customer
Would you mind waiting here for a moment?