"Plato also seems to have held such a view, where he wrote in The Republic that "philosopher kings" should lead city-states in a sort of oligarchical system." The progression, or lineage, of "cities" (men) in the Republic is as follows: aristocracy, timocracy, oligarchy, democracy, and tyranny. (Remember that it is a degradation.)It seems you meant aristocratic when you said that Plato advocates an "oligarchical system." This is an important difference. But again, is it Plato or Socrates who seems to advocate this un-decayed political form? Perhaps perusing Plato's Laws and Xenophon's Socratic works may help sharpen the boundaries between the political philosophies of Plato's Socrates, Xenophon's Socrates, Socrates, and Plato.
The Laws is an oddly pragmatic account of the political (and does not feature Socrates). Xenophon's Socrates is, perhaps like Plato but not Plato's Socrates, hyper-concerned with the practical side of life (and politics). The dryness often associated with Xenophon's writings is largely a factor of his interest in the pragmatic. (The interest is often attributed to Xenophon rather than Socrates.)
Regardless, I've heard and read countless interpretations of the Republic that claim Plato advocates aristocracy, democracy, timocracy, etc.. Even if we can disregard the setting of the Republic (it takes place during the height of the Peloponnesian War--probably at the time when Thrace joined sides with Athens, after Pericles’ death, a ruler Thucydides calls the “first citizen” of Athens, and before the rule the thirty tyrants) and the historical situation that Plato lived in (a world without Socrates, a defeated Athens, etc.), we still cannot disregard Socrates's audience in the dialogue. His main interlocutors are Glaucon and Adeimantus, Plato’s two brothers (all three are sons of Ariston-- sons of the best). They, as do Cephalus, Polemarchus, and Thrasymachus, exhibit certain characteristics of the forms of "cities" that Socrates speaks of. But of course, the forms cities are really the forms of men (but they look at cities so as to see a men's souls more clearly). --Hence the laughter at the beginning of Book V. Plato knows intimately that the multi-colored cloak of democracy can so easily lead to tyranny. It is the very nature of democracy to proclaim liberty and equality for everyone, including giving freedom and equality to tyrants. So it is in the democratic principle of indiscrimination that leads to the demise of democracy. (This is a pertinent question in political philosophy: If a political system guarantees the freedom and equality for all its citizens, what do we do with those citizens who seek to discriminate against others--either in act or speech?) But, of course, in the Republic, the tyrannical Thrasymachus is constrained by the democratic Polemarchus (and others), and defeated by the arguments of Socrates. He is silenced. This interaction takes place entirely in the first book of the Republic. But there is a somewhat parallel sequence in Books VII and VIII. Democracy is dangerous. But is Plato advocating against a democratic form of government? Or is he advocating against a democratic soul? --Or neither. --Or both?
Now what did Socrates think? Do we mean as an historical figure or literary figure? Both questions seem impenetrable. (Similarly, who knows what Plato actually thought?) But, of course, we haven’t even talked about Plato’s Statesman. (Personally, I’m inclined to think that Plato’s own political philosophy is most truthfully presented in the Statesman and the Laws.) But perhaps the most lucid, most practical, expression of Plato’s political philosophy can be found in his Seventh Letter. In it, (if I remember correctly), Plato claims the second best form of government (to the rule by the philosopher king) is the rule of just law. We might call this “second best” form of government a constitutional government.
Aristotle says, in his Politics, that the preferred system of government is of a constitutional form. That is, a government that is ruled by laws. Thus, it seems that Aristotle and Plato shared a fondness for “just” law. How we come to what is a “just law” is another story. But this is where the Republic and Statesman could help us.