Counterpart Theory, Quantified Modal Logic, and Extra Argument Places

We can couch our modal statements in the language of modal logic (sometimes, anyway) and then have recourse to possible worlds to explain the semantics of that language. Or we can proceed more directly, speaking explicitly of possible worlds from the start. Those who prefer the second course, as I do, have a choice to make. To say that there might be blue swans, for instance, we might provide our everyday descriptive predicates with extra argument places and write