Can a prepositional phrase modify an adverb?

I would be more inclined to see "close to" as a unit, a kind of compound preposition. Opinions may vary.

Edit: It occurred to me later that this interpretation might be questionable, on the basis that we can say things like "How close was he to you?".

You keep finding grammatical oddities. Keep it up."Stay close to me" is equivalent to "Stay near me." That makes me reluctant to parse "close" away from "to", or to see "to me" as a prepositional phrase. This leaves "me" out in the cold because I don't know what to call it in "near me", which you could say is really "near to me", but it really isn't. Sometimes you just shrug your shoulders and

fire1

A. Stay close to me!
I think that, in sentence A, the prepositional phrase "to me" grammatically modifies the adverb "close", because without "close", "Stay to me!" isn't correct English.
Am I right?
If so, is it possible to use a prepositional phrase to modify an adverb like in A?

"to me" is the complement of the adjective "close".

fire1Stay close to me!

I would say that the PP "to me" is a dependent in the adverb phrase "close to me", where "close" is the head of that phrase and the prepositional phrase "to me" its complement. In other words, the adverb "close" licenses (allows) that sort of dependent, here: the PP "to me".

You can't say, for example, *close s