We have examples already. In psychology, for example, we moved from the Classical-natural-history approach used by people like Freud and Jung of "here are some theories I have concocted out of whole cloth based on a handful of anecdotes and personal observations"1 to a field that actually conducts a lot of methodologically-sound studies with decent qualitative and quantitative analysis (even if many of the famous experiments, such as the Stanford prison experiment, are bunk).
Sociology has pretty much always attempted to be quantitative, though experimental design there is difficult and again the quality of work varies tremendously.
Anthropology is difficult to "harden" precisely because it emphasizes methods, such as ethnography and contextual inquiry, for which it's very difficult to apply the usual epistemological controls of scientific method (blinding and so forth), and which often necessarily use small sample sizes. (An investigator can't live intimately with a few thousand people.)
Personally, I think there's plenty of value in the "soft" social sciences and the humanities, and I wouldn't want to try to constrain them to scientific epistemology. Having harder branches of them is also useful, of course. There's benefit to both.
1Which is not to say there's nothing useful in Freud's thinking. He started one of the great self-critiques of the Enlightenment and the presumption of rationality. I believe he's right about the existence of an unconscious, even if the details in his model are highly suspect, and about the unity of libido. He's probably right, if for the wrong reason, about something akin to the "death drive". Jung, on the other hand, seems like just a bunch of crypto-religious magical thinking, but I admit I have read little of the primary material there. I won't try to get into Lacan or Kristeva or the others in a Reg comment.