ていただけませんか

A polite, deferential request meaning “Could you please …?” It asks someone to do something for the speaker.

Used when making a polite request, including in formal situations or when asking a favor of someone you do not know well. It is more deferential than てもらえませんか; the negative question makes the request less direct.

• 〜ていただくN4「〜ていただく」 can also describe a favor you have already received (e.g. 「先生にチェックしていただきました」); 「ていただけませんか」 is just one of its request forms, made softer by the negative question.
• てもらうN3「てもらう」 is neutral in register and can describe receiving favors or make requests as 「てもらえませんか」; that request form means the same as 「ていただけませんか」 but carries less respect, so use 「ていただけませんか」 with superiors or elders.
• させてくださいN4「させてください」 asks the other person to let you (or your side) do something, while 「ていただけませんか」 asks them to do it themselves — the actor is reversed, so they are not interchangeable. The former is more direct; with superiors, prefer 「させていただけませんか」.
• ませんかN5「ませんか」 attaches to the ます-stem and is used to invite someone (often to do something together) or to politely ask whether something exists; 「ていただけませんか」 attaches to the て-form and humbly asks someone to do something for you, so the two cannot be swapped.

〜ていただく expresses receiving the favor of someone’s action, while ていただけませんか uses its potential-negative question to make a request; てもらう expresses receiving that action without the same humble form. させてください asks permission for the speaker to act, whereas bare ませんか can propose or invite an action without expressing the request as receiving a favor.