to go through channels: to send a request through the normal way
This idiom can be used with the adjective proper.
to turn over: to place upside down (S); to flip, to turn upside down; to pass or give control to someone (S)
to cover up: to conceal, to hide (S)
This idiom is used for events that are potentially embarrassing to one's reputation, as well as against the law. The noun coverup derives from this idiom.
to kick the habit: to stop a bad habit
to make up with: to resolve differences with
This idiom is used for differences of opinion between friends and lovers.
to make up: to meet or fulfill a missed obligation at a later time (S); to create, to invent (an idea) (S); to apply cosmetics to (S); to comprise, to be composed of
Note that all of the definitions are separable except the last one.