A fact of the matter is geography here.
The Western Empire has a long frontier with Germany, a mostly fertile region, if a bit cold and damp by Roman standards, that can support a fairly large population. It isn't steppes, so it's "barbarians" are pretty settled and organized, especially compared to the brief rises and falls of steppe empires. So, the Germans had the ability to carve out much of the west and create successful, long-lasting kingdoms out of it.
Meanwhile, the East has a vastly different situation. To the South, they have the Arabs, which are probably your best chance for this. The Eastern Empire even had a similar system of federate Arab troops to the west with the Ghassanids. The problem is that Anatolia is so easy to defend that the Eastern Empire can hole up there and wait out invasion. However, in a situation similar to the fall of the West, you'd need Romans to be heavily involved in the collapse, so unlike early medieval Theme-based Fortress Byzantium, and more like intrigue-ridden Arles, Milan and Ravenna.
I think probably the best way to do this is to have the Goths essentially take over the Roman Empire via Theodosius, the son of Galla Placidia and Atualf. With the Goths acting as the Isaurians did for the east (a tribe of our own "barbarians" who have much more interest in Imperial survival rather than collapse), the Empire might be able to prevent the utter disaster that was the Vandal invasions of Africa. Meanwhile in the east, population pressure in Arabia (which could have caused an invasion to happen with or without Mohammad) might allow something similar to happen to Egypt, Syria and Anatolia.