There doesn't seem to be much of a fanfic tradition for literary SF. I'm not sure why; there's plenty of shared universe action going on, but it seems to be more a professional than an amateur phenomenon.

The obvious answer would probably be that literary SF doesn't have enough long-term focus on characters to be appealing to fanfic writers, but there's enough setting- or conceit-based fic in other genres that I'm not sure how seriously to take that. People usually don't write Lovecraft fic because they want to read more about Randolph Carter, for example.