As in the title. Does the expression a couple of always have to mean exactly two (like a pair of) or can it mean more (things/objects)? I know a couple, at least in one of its meanings, means a pair (like the happy couple) but as an amount specifier does it also always mean exactly two?
Formally: Yes. It refers to two items of a type. In that sense, not only does it always mean two, but the type of those two items must always be the same.
A couple of people, A couple of fruits.
However, when used informally; it can refer to any indefinite small number.
That said, as your question is referring more closely to meaning as opposed to definition, I would be inclined to accept the more loose association of the word as being to express a small number of things of quantity unknown.