The "parallel-universes" concept states that, as time goes on, a choice would start new universes -- all of the possibles, happening in parallel-universes, thus no option getting totally lost in history. The Islamic concept of phenomenal time is incompatible with such "parallel universes" ("many-worlds").
First of all, some "choices" may not be true choices, although we might have thought so, while facing the "choice." Thus, the statement of such "many-worlds" hypothesis, if suggests that all of what we were pre-occupied with, may have been living in some other universe, I oppose that even in the case of future, because we know that Allah crafts the possibles (qader, written in lewH-ul-maHfooz), not always with such full options. While choosing from the possibles (qader) our specific fate (qaDa/qaza), we may have been constrained by a few restrictions, too -- (wish or not) inescapables (isabet/musibet) targeting you, either from the start, or after you have chosen a specific path. Hadid(57):22
So far as I know, the Islamic literature on qader (the possibles), suggests that the past is single, while the future has branches for options. Living & knowing is toward pruning some of the priorly-possibles.
Would souls multiply to the "parallel universes?" That does not sound Islamic, at all.