~てくださいませんか (honorific request)

A layered polite request: te-form + くださる (honorific 'give') + interrogative ~ますか or negative ~ませんか. Literally 'will/won't you kindly do X for me?' Extra-polite alternative to ~てください, appropriate for requests to clients, staff, superiors, or in formal settings. The negative form (~ませんか) is slightly softer; the affirmative (~ますか) is slightly more direct.