コートを持ちましょうか。

code; cord; chord

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.

to hold (in one's hand); to take; to carry; to possess; to have; to own; to maintain; to keep; to last; to be durable; to keep; to survive; to take charge of; to be in charge of

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