Use this when making a request of a client, superior, or outside party and you want the softest, most deferential framing available — typical of business email, phone calls, and negotiation. It layers 〜ていただけますか (humble "could you give me the favor of") with でしょうか, which converts the direct question into a tentative inquiry, so the request reads as "might I possibly ask you to…". Strictly speaking ますでしょうか is criticised as 二重敬語, but it is thoroughly established in business register; in neutral or internal contexts 〜ていただけますか / 〜ていただけないでしょうか are enough.