During the existence of the Western and Eastern Roman Empires, they were not seen as separate states. They were one Roman Empire, the two halves only governed by two emperors out of political expediency. That and the Eastern Emperor just did not want to bother with the less valuable West.
If the West didn't fall and East didn't lose most of its territory, neither of which were inevitable, this probably would have been an advantage over the previous, unitary Roman Empire--outside enemies keep the Roman emperors as allies most of the time, while having those separate emperors makes the territory easier to administrate.
In a scenario where an ambitious Eastern Roman Emperor conquered Persia, could he create a third empire out of the new conquest?
If Italy and Africa became wealthy again, would Gaul and Britannia be split into another empire?