Pretty hard to do, as the East was the economic engine of the Roman Empire. Invasions alone won't do...part of the reason why the emperors moved to Byzantium was to be closer to the front lines against the Persians, Huns, etc.
What needs to happen is for the invasions to be concentrated in the East, massive crop failures in Egypt and widespread revolt in the East while the soft underbelly of the Empire that is the West remains unmolested.