I fail to see the relation between "branching" (or however do you want to call the feature that separates the standard universe from the multiverse, I let you pick the name for it) and the unitary evolution of the wave function.

As for your question: I don't know. Let's say the Schroedinger equation is actually not perfectly linear and there is spontaneous collapse which happens quite rapidly for a system with N~10^30 particles. Now what?