What do you want out of a framework? What should it do, and why is agreement important?
I will quite happily construct a model to try and capture the behaviour of real-world social problems, drawing on a variety of methods and disciplines. I'm not sure I need agreement from any other party to do that. How well it describes or predicts real-world events is an empirical question.
When I see people talking about privilege, it generally isn't because they want to go out and solve social problems, but because they want to show how sophisticated and moral and liberal they are, or to identify other sophisticated moral liberal people by engaging in exclusive dialogue with them. If that's what such a framework is used for, I'm not entirely sure the absence of one is all that important.
What do you want out of a framework?
I want analysis that tells me what to do to create the changes that I want in society. Not just imposed top-down, but deeply settled as part of how society works - on the level of "get a job" or "be polite." The sort of thing "equal-pay-for-equal-work" aspires towards, but maybe hasn't reached.
The privilege-framework says that the way to do that is to call out privilege when you see it. If someone makes the non-consent joke the blogger highlighted, say "Wow! That's not right.&quo...
As Multiheaded added, "Personal is Political" stuff like gender relations, etc also may belong here.