The Langlands correspondence over a function field matches irreducible $n$-dimensional Galois representations with cuspidal irreducible automorphic representations.

My question is: Is there any idea or conjecture around, how this could extend to reducible representations?

As automorphic representations are semisimple, they don't allow for non-trivial extension, which however on the Galois-side can happen. Maybe there are ideas from geometric Langlands (of which I don't know much) that can help?