One of the greatest ever Historians of Rome, the great Friedrich Munzer, showed one century ago, in his masterpiece Roman political parties and families, how the roman regime and ruling groups, evolved and worked.
And from his work and other sources (especially Badian and his Foreign clientelae work), it is possible to understand the pattern that progressively led from what is rawly called the monarchy and what is rawly called the republic.
Most telling is the case of the gens Fabia in the first years of what is called the republic. For 7 years, from 485 BC to 479 BC, there was a Fabius as consul. This was unprecedented since 509 and the fall of the Tarquins and never happened again until Augustus' 8 consecutive consulships from 30 BC to 23 BC.
What this shows is that the monarchy was a clan dominating the State as well as the republic often was a clan or an alliance of clans dominating the State, although for a much shorter time.
And the leading clan or alliance used its preeminence in the State to conclude family and political alliances with foreign aristocracies, some of whom moved to Rome in order to consolidate or strengthen their position at Rome.
There are archeological finds showing there were other Tarquins than the 2 kings and than the sons of Tarquin the proud. And these finds showed that some of these other Tarquins held commanding positions either at Rome, or at other location that were tarquinian "possessions".
The Licinii, originating from Etruria, probably came to Rome in the wake of the Tarquins. It is probably because they were marked as "tarquinians" that they were not reckoned as patricians (which only meant being reckoned as enjoying full political and religious rights) but were the most prestigious and powerful plebeian aristocratic family as early as the late 5th century BC (as is evidenced by the fasti and the legend of the 2 daughters of a Fabian princeps).
The Claudii were sabine foreigners the head of whom was integrated as patrician (the lesser families of the gens Claudia were integrated with mere plebeian status, like the Claudii Marcelli) in 504 BC because the clans dominating Rome were then so weak that they were ready to pay such a high price. From the mid-5th century on, Rome felt less weak so it never again granted patrician status to foreign aristocratic allies that were integrated in the City of Rome.
The evolution is that there was a social evolution that made more and more difficult for a single clan to hold supreme political power at Rome for a long time.
And this trend went on until the gathering of the immense resources of the empire made It possible for one aristocrat to reestablish a strong and lasting monarchic power for one individual and his family.
