Patrician families claimed descent from the original couple hundred senators under the kings. That's all, end of story. The patrician order was expanded to several times in the early history of the city by the inclusion of noble families from foreign subject cities--notably the Albans and the Sabine (which is where the Claudians, for example, came from), but it always remained a small group. We know the names of something like fifty patrician families in the earliest period, but by Caesar's lifetime only fourteen still had extant patrician branches--the others had either died off completely or only had plebeian branches left. This is because the patrician order was not easy to maintain and additions after the earliest period were very rare. Under the Twelve Tables patricians could not marry plebeians, and though that was overturned almost instantly very few patrician families were willing to intermarry anyway. After Caesar and Augustus greatly expanded the patrician order with the inclusion of many notable plebeian families even the basis of ancestry becomes more or less irrelevant

We should not think of the patricians either as the wealthy or political elite. They do not represent the senatorial class in any way, shape, or form. The Conflict of the Orders had largely ended by the end of the 4th Century, BC, with a decisive plebeian victory, and although conflicts continued until the 3rd Century, BC these were largely minor rights. By the end of the 4th Century plebeians elected the tribunes and plebeian aediles, could intermarry, could hold the consulship (although personally I believe this was already a law--of the original consuls, Brutus was plebeian, since the gens Junia was certainly mistaken when they claimed to have been a patrician clan demoted to plebeian status), had to hold by law one of the two consulships each year (the other could be a patrician, though was not necessarily), had to hold at least one of the censorships when the office of the censor existed (usually every five years), and had to hold at least half the priesthoods,. By the end of the 3rd Century, measures passed in the Concilium Plebis became law, not just those passed in the Comitia. Plebeians could already hold senatorial magistracies other than the consulship (if we are to believe that they couldn't hold it in the first place), so we know they could sit in the senate. Indeed, by Caesar's lifetime and already by an early date the majority of the senate Wed composed of plebeian families--Cicero, Pompey, Antony, Crassus, Cassius, Brutus, and Cato, to name just a few, were all plebeians and most of them came from extremely old senatorial lines. The fact that a plebeian consul had to sit each year meant that at least half of the nobiles, those with consular ancestors, who represented the highest social echelon of the senatorial class, were in fact plebeian. Nor were plebeians restricted from extraordinary wealth--indeed, Crassus, who claimed to be the richest man in Rome, and Pompey (who probably actually was, until his death) were both plebeians. An entire unofficial social class, which became officially recognized under the Principate, the equites consisted of plebeians who had the money to run for senatorial magistracies but had no actual interest in politics and did not--many of these men, like Cicero's father and Cicero's friend Atticus, were absurdly wealthy, far wealthier then many patricians