Wittgenstein originally put forward the 'picture theory of meaning', which propagated that a given sentence or word is meaningful insofar as it corresponds to a fact or 'picture' of the world. The only statements that could be meaningful were true statements, and the only way a statement could be true is if it corresponded to some 'picture' or facts.
Wittgenstein would later substitute this view of language in favor of a semantic system with more pragmatic overtones. So instead of a sentence or term possessing meaning in virtue of it referring to some picture, it possessed meaning insofar as it possessed a certain use. And use, unlike reference, is context-dependent.
This inevitably leads to what Quine would later philosophize about the nature of meaning, that it is indeterminate. If it is by the context of our behavior (or any other context for that matter) that meaning is determined, then there are countless ways that we can interpret any meaning. The test seems to have the consequence that meaning is not truly determined in an absolute way, that there simply are no truth-conditions for any given sentence.
But it seems questionable that this analysis is exhaustive, especially considering its cost. We can imagine, for example, that we instead follow the medieval school of logic, which divides signification (the act of meaning) from supposition (the act of reference).
The medieval theory held that reference, unlike meaning, was context-dependent. Whereas earlier Wittgenstein seems to have believed that meaning could be hashed out in talk of reference alone, the medieval theory always thought, with later Wittgenstein and typical modern thought, that reference was an insufficient determinant of meaning.
But unlike later Wittgenstein and his proceeding troop of followers, the medieval theory held that meaning was determined immediately by the concept of an object and mediately determined by the ultimate significatum, which is the object itself. Reference, or supposition, could vary according to what meaning one had in mind, be it immediate or mediate. To say that meaning is 'context-dependent', for medieval thinkers, would be to confuse what 'meaning' is, for the meaning of a thing, insofar as it is, is known instantaneously in the very fact that the thought of it is entertained; meaning for the medievals, to put it another way, was inseparable from the act of meaning, the principle act of thought and understanding. This differs from modern presumptions which seem to believe the only way meaning can be determined is by a theory of reference.
Aside: What then, it might be asked, influenced Wittgenstein to believe a pragmatic semantic theory could account for meaning? In the hands of Quine it has been found that it can't. And long before Wittgenstein it was held that reference wasn't the main determinant of meaning anyway (and neither was context-dependent 'use' either), so it seems that there aren't only two possible determinants of meaning, be it rigid reference or context-dependent use. There is the option to believe that meaning lacks a condition under which it is known, not because meaning is indeterminate, but because the relation between thought and object of thought is not contingent; meaning under this semantic theory simply is.
To bring in the original and more modest question, does Wittgenstein think that his treatment of meaning is exhaustive? Or does he allow (at least in theory) that one can have a different approach to meaning, holding that it is neither reference nor use that determines a given statement's meaning?