The Fourth Wiggins

As I've mentioned before to some of the local fangirls, I'd really like to participate in a book club-style group aimed at fanfic. I'm trying to figure out how it might work.

I imagine participants all reading a given fic, then getting together to squee, bitch, and meta about it.

I imagine participants reccing fics that relate to a particular theme to be discussed. (crack fic, women in leadership roles, crossovers, etc.)

I'd like it to be multifandom, but how then to choose fics for everyone to read?

I imagine it'd be best if authors refrained from participating in discussion about their own fic. I'd want the group to be for talking about readers' experience of a story. I think that engaging the author about it should be done in the author's space.

Only fanfic? Would a broader fanworks approach be more or less appealing?

If something like this already exists, please to be link-sharing?