Presumably, the number of 'possible' states of the universe is the exact same as the number 'possible' alternate universes. (Edit: unless you are using two different meanings of 'possible')

The question of convergence then simply boils down to: Are there any possible states of the universe that can arise from more than one prior state. Based on my limited quantum mechanics knowledge, it seems the only place this might be able to happen is in black holes: https://en.wikipedia.org/wiki/Black_hole_information_paradox