What if the Roman Republic still rises to become the superpower of the Mediterranean of OTL, then collapses into civil war, anarchy, and despotism, more or less as it did OTL -- but then, instead of its influence being bound together under the power of a single Principate as OTL, the "empire" of the former republic remained carved up by warlords, not to be reunified for at least a couple of centuries.
How is history in the western world changed by this? Try looking at this in the broadest possible light, over the longest time possible; for example, does this post-collapse world effectively revert to a new Hellenistic Era? Even more broadly, is the legacy of Rome in western history (millennia from our PoD) now greatly diminished?