N4
ていただけませんか
Won't you, Could you please (Humble request)
すみませんが、後ろに乗っていただけませんか。
I am sorry but, could you please sit in the back.
Explanation
「〜ていただけませんか」 is a very polite request to an elder, boss, client or someone you have just met: 「もう一度説明していただけませんか」 (Could you explain it once more?), 「日本語のレポートを直していただけませんか」 (Could you correct my Japanese report?). Literally it is 'could I receive your doing … for me?', with three layers of softening: humble, potential and negative question.
Mixed up with
Politeness of requests: 「〜てくれない？」 is for friends; 「〜てください」 is generally polite but a bit directive; 「〜ていただけませんか」 is for elders and superiors and is always safe.
The other person does the action, and I receive the benefit.