Drop in on (help!)

It's an idiom.

It doesn't mean to literally "drop" or "in" or "on"

Do you happen to know why there are two prepositions? A student asked why it uses both "in" and "on". They asked if it was working as an adverb or a preposition. My gut is telling me neither, that they're just part of the idiom/expression but I can't explain why. Is this one of those, "it just does" situations?

You are completely over analyzing it. It's an idiom.

"Drop in" is used as a verb meaning "visit".

It's a phrasal verb, which is an idiomatic phrase consisting of a verb and another element, typically either an adverb, as in break down, or a preposition, for example see to, or a combination of both, such as look down on.