This is very hard to imagine. The only area capable of providing the money, manpower, legitimacy, etc. needed for a state to survive was modern-day Andalusia (e.g. the southern region of Roman Hispania). There is simply no comparing the West with the East: the former was generally unsettled, heavily rural, had little to no naval power to speak of, and comparatively lacked cosmopolitanism, as the Romans had set out quite viciously to suppress the only reasonably far-reaching institution there, Druidism. In comparison, the East had been built up by repeated Empires like the Seleucids, Ptolemies, Macedonians, Achaemenids, etc. It's position along the Silk Road also enabled it to reap benefits the Western portion of the state simply had no access to, while the existing of a relatively unified nobility gave the East a much stronger chance at survival than its Latin "counterpart".