Scenario 1: What if Aurelian hadn't become Emperor in 270, and the Roman Empire had not reconquered the Palmyrene and Gallic empires? Would these breakaway states have been able to survive in the longer term? Does someone (Diocletian, Constantius, Constantine) come up later and retake them? If not, what happens when the barbarian invasions of the late 4th and early 5th centuries start? What effect does this have on the spread of Christianity? Does the remaining empire stay together long?
Scenario 2: What if, on the opposite tack, Aurelian hadn't been murdered in 275? He got pretty hosed with the actual circumstances of his assassination, IMO. Does he manage to stop the crisis early, without tetrarchs? Is there an alternate governing system that can function? And again, how does this impact both Christianity and the survival of the Roman Empire?