For any claim X, exactly one of these is true:
1) X is possible - compatible with the evidence so far.
2) X is impossible - there's a contradiction between X and the evidence so far.
That means asserting the possibility of something is harder than you think. For example, if Bob says: "Epiphenomenalism is possible, therefore <far reaching conclusions>"
Wait, Bob, did you just say it's impossible to find a contradiction between epiphenomenalism and anything else you know? That's an awfully strong claim! You got any evidence?
Bob pulls back: "I meant only that X sounds plausible to me." But that's a fact about Bob's limits of reasoning, it doesn't support the far-reaching conclusions anymore. For that you need to justify (1) over (2), not just assert it.
I think you're holding Bob to an impossible standard. When you say things like " it's impossible to find a contradiction between epiphenomenalism and everything else we know ", you're implying that Bob is overreaching unless he knows and indexes "everything else we know". Bob's description of plausible (compatible with everything I know, and with everything you can point out to me that I should know) seems closer to a reasonable colloquial use of "possible".