Rather hard to do.
For having a new Chuch, you'd need to have at least dogmatic differences, and that's not really going to happen with both popes rivaling of orthodoxy to demonstrate they're the real shit.
You didn't have pre-existing divisions, as in Greek and Latin churches that became more and more different after the VIIIth/IXth centuries, and you didn't have radically new theology as Reformation : it was essentially a political crisis, as in a civil war would probably not end with two states living side by side.
Critically not with resolvement of Schism that was a leitmotif not only for Churches but as well for kings, emperors, and so on, as in a possible really good legitimacy and fame boost.