Second Temple Judaism?

So if Jewish people in the Persian period have multiple temples, then at what point can we speak about second, second, third, fourth, fifth temple Judaism? Right, right. And that's a case where it could be our theory who runs up against some data that it fits fairly awkwardly. So we need to reconceptualize how do we talk about early Judaism in ways that don't make Ella Fintini kind of exotic, bizarre or phenomenon.