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Could you (do sth)?

Would you mind (doing sth)?

Can you help me, please?

Could you give/lend me a hand?

Would you like...?

How about ....?

Fancy...?

I´ll do it for you.

Shall I help you to (do sth)?

How can I help (you)?

Thank you very much. That´s very kind of you.

That would be lovely, thank you.

Could I...?

Is it OK/all right if I...?

Do you mind if I (did sth)?

Would you mind if I (did sth)?

Would it be OK if I (did sth)?

I was wondering if I could...?