コートをどうぞ下へ置いて下さい。

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.

please; kindly; I beg of you; by all means; feel free; you are welcome; here you are

below; down; under; younger (e.g. daughter); bottom; beneath; underneath; just after; right after; inferiority; one's inferior (i.e. one's junior); trade-in; preliminary; preparatory

indicates direction or goal (e.g. "to")

to put; to place; to leave (behind); to establish (an organization, a facility, a position, etc.); to set up; to appoint (someone to a certain position); to hire; to employ; to place (one's trust, one's faith, etc); to bear (in mind etc); to put down a tool (e.g. a pen) hence stopping what one is doing with that tool; to take in (boarders, etc.); to provide lodging in one's house; to separate spatially or temporally; to do something in advance; to leave something in a certain state; to keep something in a certain state

to give; to confer; to bestow; to kindly do for one; to oblige; to favour; to favor