Speaking for myself, I find the privilege framework to be the one lacking in nuance or pragmatic application. I use the term "unilateral" because its core mechanic appears to be "person A has power person B doesn't, and person B suffers as a result". Coming from a game-theoretic perspective, which routinely deals with unexpected and perverse outcomes from agents being given different sets of choices, this seems crude in the extreme.
On the subject of multidimensionality, I've read up on intersectionality in good faith, and made an effort to engage with it, but it seems to boil down to multivariate analysis, only instead of using data, simply making stuff up.
So we have no agreed framework? That . . . kinda sucks.
Is there anything we can do about it?
As Multiheaded added, "Personal is Political" stuff like gender relations, etc also may belong here.