* = Zombies remain metaphysically possible because the natural laws could have been different. If you value your inner lights, be thankful they aren't!
It's not entirely clear what substance dualism involves. But here's one possible view in the vicinity: brains and other physical stuff are (even nomologically) insufficient for consciousness. To be conscious, one needs special soul-stuff, bestowed perhaps by a supernatural
Now, that view sounds crazy. But it also sounds a lot like the sort of thing the average theist in the street might say. (Right? Or am I being uncharitable here? Average street-going theists have been known to say many a crazy thing...) Anyway, the particular problem I want to highlight is that this kind of substance dualist cannot respond to skepticism about other minds by appeal to the argument from analogy I offered above. The "relevant similarity" is no longer merely physical/behavioural. These latter properties offer the dualist no evidence whatsoever that there is anything mental going on in addition, since the evidence is equally consistent with zombiehood, which is a possibility they're just as happy to grant.
Is there any escaping this problem for the dualist? If we grant the general (nomological) possibility of zombies, then it's hard to see any basis for ruling out the possibility in particular cases (excepting our own, of course). Perhaps you could appeal to a benevolent God -- but wouldn't he only grant consciousness to lives that are worth experiencing? The theist should then expect that people apparently suffering outrageous hardship are in fact zombies. (Have I hit upon a novel solution to the problem of evil? Solipsism!)
But perhaps substance dualists are not committed to the nomological possibility of zombies? I'd need an explanation of what their view involves instead, then. (I have trouble making sense of the claim that physical substance could nomologically necessitate the existence of corresponding mental substance. Would they really be two distinct substances in that case?) Do tell...