So I have one game I'm working on with a co-chef based on the random threads, but I also can't seem to get my brain to leave the Mimic ingredient alone.

Specifically, I like the idea of a game in which the roleplaying challenge IS to mimic - to impersonate - someone.

So I put MIMIC, DOCTOR and COYOTE together, stew it together with the Turing Test, Mafia/Werewolf and critiques of James Cameron's Avatar, and here's where I'm at:

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The Coyotes are a gang, or a tribe, or a race, or a species. They're close knit, mysterious and "savage".

Your funding depends on you infiltrating them.

You play online, or via some other anonymous medium. Most players form the Coyotes, and workshop together their culture and mannerisms. The Doctor then observes them interact, and makes notes.

This is followed by a series of scenes in which the Doctor attempts to pass himself off as each of the Coyotes in turn. The Doctor and the real Coyote enter the scene in a randomised order (either first or second) and interact with the rest of the Coyotes. After the scene is over, the Coyotes aim to discern which was the real Coyote and which the fraud - they hold a secret ballot.

How do you keep the posts anonymous, again?

How to bring in the theme?

I could have the Coyotes holding some secret knowledge that the Doctor has to discover....

If it was going to be played in a house or con setting,(in person)
you could keep a great deal of anonymity by following these:

a) the Coyotes do not use or recognize the use of individual names. On a meta-level, this means that when playing, they also can't name players, or create names for them like "big tall", for the tallest person in the group.

b) never have the entire group together at once - perhaps the outsiders would get some pre-game somehow, similar to werewolf / mafia, but when play is underway... ok, i'm explaining this wrong.

We're playing at my house. I have a large living room. Anne is running it. She knows who's Coyote and who's outsider.
The group is distributed through the house, or is in a fairly dark room with their heads down & eyes closed, and Anne pulls them out first one, then a second. Those two interact - they decide the, say, five things that coyotes do that show that they're coyotes. Then the first sits down again, eyes closed, and Anne brings in the third player.

Now, third player is also a Coyote, Anne knows this. so second player shows third player the five moves, but first and third players don't know that one another are coyotes - and then second sits down, and Anne brings fourth player to learn from third. Of course, the precision that Coyote 1 (C1) taught C2 is breaking down a little bit by now, and by the time C8 is teaching C9 the five signs of being a coyote, there are marked differences.

That's all setup. The outsiders are never brought into that room to learn from Coyotes.

Play would have groups of two players meeting (more work for Anne) and trying to discern if one another are coyotes. Maybe after groups of 2 you have groups of three, or jump immediatly to groups of 4 - And there's not neccesarily an outsider in there, but there MIGHT be...

You know, i just re-read your OP, and i have foolishly swerved away from what you were talking about.
Your rules sketch is elegant, mine at present is terribly unwieldy. Perhaps you'll find some use for it, though, so i'll leave it.

So the game consists of the Coyotes creating norms and the Doctor trying to adopt them?  Neat!  What would the fictional context be or this process?  Would there be any individual character differention or would it be more of a social strategy-style game?