ていただけませんか details

write + (and…) + could you please do ?

kaite itadakemasen ka

could you please do (for me)?

meaning: could you please write

この荷物にもつ、少すこしの間あいだ見みていてもらえませんか。

kono nimotsu, sukoshi no aida mite ite moraemasen ka.

Could you keep an eye on this bag for a little while? neutral

すみませんが、会議かいぎの日程にっていを変更しへんこうしていただけませんか。

sumimasen ga, kaigi no nittei o henkoushite itadakemasen ka.

I'm sorry, but could you please change the date of the meeting? formal

Examples

could you do (for me)? — deferential request

この荷物にもつ、少すこしの間あいだ見みていてもらえませんか。

kono nimotsu, sukoshi no aida mite ite moraemasen ka.

Could you keep an eye on this bag for a little while? neutral

すみませんが、会議かいぎの日程にっていを変更へんこうしていただけませんか。

sumimasen ga, kaigi no nittei o henkoushiteitadakemasenka.

I'm sorry, but could you please change the date of the meeting? formal

お忙いそがしいところ恐縮きょうしゅくですが、資料しりょうに目めを通とおしていただけないでしょうか。

o isogashii tokoro kyoushuku desu ga, shiryou ni me o tooshite itadakenai deshou ka.

I'm sorry to bother you when you're busy, but might you look over the materials? formal

ていただけますか — positive question — a notch more direct, still fully deferential
ていただけないでしょうか — the softest tier — written requests and delicate asks
てもらえませんか — plain もらう for humble いただく — everyday politeness without the deference

It is a real question only in form: the felicitous answer is doing the thing, not はい・いいえ.

てくれませんか
Same negative-question request, different receive-verb deference — いただけませんか humbles the speaker and owns business speech and email; くれませんか is the spoken default among equals and reads presumptuous aimed upward.
てください
Both request politely, but てください instructs while ていただけませんか asks whether the favor is possible — teachers and signage use ください downward; requests aimed up the hierarchy switch to いただけませんか.