Some of Rome's greatest external threats were the Sassanids and the Germanic tribes. The first were a powerful, organized entity that required the lion's share of resources to combat (a task the Romans mostly succeeded in accomplishing) while the second, while underdeveloped and weak at first (features which made it pointless to conquer them early on), eventually evolved into a society that, when pushed on by migrations from the east, managed to take over everything west of Thrace (obviously also helped by the other problems facing the empire at the time - plague, crop failure etc etc).
However, there was a short, fleeting moment when both of these adversaries of Rome were in position to be defeated - and this was during the reign of Alexander Severus.
This was right before the crisis of the third century, meaning Rome's economy, population base and strength relative to that of its neighbors were close to their peak. What made the situation so favorable was the fact that, at the the time, the Persian state was undergoing one of its worst civil wars (something Rome usually was very good at taking advantage of), a civil war that pitted the Parthian dynasty against the up and coming Sassanids. Meanwhile, the Germanic tribes had been steadily transformed by centuries of contact with the Roman world, and were now much more appropriate targets for conquest and romanization of the ruling elite.
Had Alexander Severus' campaign in Persia been successful to the extent that the major population centers were razed, northern (possibly also central) Mesopotamia directly annexed and the rest divided between small, tribute-paying states upon which Rome kept a close eye, then THE major stress plaguing the Roman world would have been eliminated for at least a generation or two.
Likewise, if his campaign in Germania would have been successful, it would have meant butterflying away from history the very groups that spelled the death of the western empire. While there were obviously other barbarians further east of the Elbe, these too would need centuries of contact with the Roman world to develop the kind of society needed to conquer and hold Roman lands and defeat Roman armies, time they would not really have by the time the (probably climatic-driven) Great Migrations start rolling.
If both of these are as successful as postulated, and if they are coupled with an even broader monetary reform then that of Alexander Severus (of the kind performed by later emperors), then it's not inconceivable that the Crisis of the 3rd Century never takes place, with HUGE butterflies - trade stays strong, urbanization continues at a fast pace, the established system of local assemblies managing their own polis never gets dismantled and the general slide towards autocracy witnessed OTL is at least delayed if not stopped.
Rome would be in a much better position to weather the migrations and plagues that brought if down OTL, and would probably rebound relatively fast from them. By the 7th-8th century (once Arab migrations were repulsed), we would probably begin to see the rise of a prominent merchant/petit bourgeois class challenging the great landlords. If Christianity still becomes dominant, it likely attaches itself to Imperial power and, supported and financed by it in a time of prosperity, leads to a (slightly) more homogenous culture for the peoples of the Mediterranean.