No Roman imperial dynasty seemed to last for very long though - in part due to the lack of a codified system of succession. Maybe adoption (as employed by various emperors) could be turned into an institution as central to Rome as the Senate, who knows; the Senate could be made to elect a crown prince of sorts out of several options picked by the ruling emperor for example.
Adoption was only employed when the emperor had no legitimate children -- the only exception I can think of is Claudius, and all our ancient sources think that he weird to make his stepson equal to his biological son and had probably been bullied into it by his wife. Even as early as the second decade AD, Agrippa Postumus was considered to have a strong enough claim to the throne for Augustus or Tiberius (it's not clear which) to have him murdered, and literally his only qualification for rule was that he was related to Augustus. So it seems that the Romans came to accept the idea of an "imperial family" pretty early on in the principate.
Personally, I reckon that the main problems with Roman dynasties were (a) the low fertility amongst the Roman elite, and (b) the lack of a clear succession law. Regarding (a), I suspect that this was due largely to the Romans' habit of using lead to sweeten their wine (this may also have had something to do with the more... eccentric qualities displayed by some of the Roman emperors), but presumably this practice would be butterflied away. Regarding (b), this would be difficult, since it would require openly admitting that Rome had become a monarchy rather than a republic, something which many senators were loth to do. If it could be done, though, it would be a great boost to stability, since it would stop everyone and his cousin declaring themselves emperor every time you had a weak or underage ruler.
As to the OP, I reckon an alt-Frankish empire might be in a good position to end up as a kind of European China... The north of Europe is basically one big plain from the Atlantic to the Urals, so there's no insuperable geographical barrier to uniting the core of the Frankish Empire (basically modern France and Germany), and a state which controlled this territory would be able to at least dominate, if not outright conquer, most of the rest of Europe.