Once upon a time there were two possible worlds that were identical in every physical or natural respect: they are atom-for-atom replicas. Two indiscernible counterparts, Fred1 and Fred2, stood in their respective doorways and gazed up at their identically overcast skies. As it happens, they then both stayed inside. This was just as well for Fred1, since if he had gone outside, he would have triggered a chain of events culminating in his being struck by lightning. Not so for Fred2, however; he could have safely stepped outside. It just so happens that he didn't. The End.
It seems a little fishy to me, but not obviously so. This may be because the story is harder to get an intuitive grip on. Someone who fully understood might experience resistance just as strong as that which we typically feel in the moral (or musical) cases which violate supervenience.
One problem with the counterfactual example is that we might be confused by the possibility of indeterminism. One might hold that worlds with identical pasts could diverge in their (actual or counterfactual) future properties because the laws of nature do not fully determine how the future will turn out. If the Freds had stepped outside, this would have triggered an indeterminacy which would resolve into a lightning strike for Fred1 but not for Fred2. Now, I'm not sure that this is the best way to understand indeterminacy. It might make more sense to say that there's only the one counterfactual shared across the identical scenarios, in which it's indeterminate whether the Fred in question gets struck by lightning or not. But let's avoid such complications by instead considering a story about objective probabilities:
Once upon a time, God created two physically identical coins, which were atom-for-atom replicas of each other. But the first was a fair coin, whereas the second was biased towards 'heads'. God wanted to use them to beat Satan at gambling. As it turns out, both coins ended up yielding identical results (H,T,H,H,H,T) when tossed in identical physical conditions. You might expect that, what with them being physically identical and all. Still, only one of them was biased towards heads, so it was just bad luck that the fair coin didn't land tails more often. It was objectively more likely to do so than the biased coin was. The End.
That one sounds very weird to my ear. When the story claims "it was objectively more likely...", I'm inclined to think, "no, it wasn't!" Do you agree? If so, this interesting new class of (modality-based) cases of imaginative resistance would seem to support my claim that modality is supervenient (or at least objective chances are).