ていただけませんか is the 謙譲語（けんじょうご） (humble speech) form of てもらえませんか, which itself is the negative potential form of てもらう ‘to have (A) done by someone else’.
This structure is a combination of て (the conjunction particle), the う-Verb いただく ‘to be topped with’, the polite-negative auxiliary verb ません, and the question particle, か.
Generally, it is translated in a similar way as てもらえませんか ‘won’t you (A)’, or ‘could you please (A)’.

• すみませんが、後（うし）ろに乗（の）っていただけませんか。
  I am sorry but, could you please sit in the back.
• 危（あぶ）ないので少（すこ）しだけ下（さ）がってもらえませんか。
  Because it is dangerous, could you please back up just a little.

This construction and いただく itself can regularly be seen as 頂（いただ）く, its kanji form. Due to this kanji literally meaning ‘to be topped with’, it is just acknowledging that the person that is doing the action for you (or someone in your group), is doing so from ‘above’ (sounds more respectful).

• 雪（ゆき）を頂（いただ）いた山（やま）はとてもきれいだ。
  A snow-capped mountain is very beautiful.

Here we can see how the ‘to be topped/capped with’ meaning is used in a standard sentence.