コーヒーを１杯いただけませんか。

coffee

indicates direct object of action; indicates subject of causative expression; indicates an area traversed; indicates time (period) over which action takes place; indicates point of departure or separation of action; indicates object of desire, like, hate, etc.

one; best; first; foremost; beginning; start; bottom string (on a shamisen, etc.)

sake cup; cup for alcoholic beverages; counter for cupfuls; counter for ships, octopuses and squid

to be able to receive; to be able to take; to be able to accept; to be able to eat; to be able to drink; to be acceptable; to be satisfactory

indicates a question (sometimes rhetorical); or; whether or not; some- (e.g. something, someone); indicates doubt, uncertainty, etc.; emphatic prefix; suffix forming adjectives or adverbs; in that way