Counterpart theories are powerful thanks to their flexibility: counterpart relations are not symmetrical or transitive, and one can apply more than one counterpart relation to one object. This is used to analyze metaphysical puzzles, but it also gives rise to an objection: this flexibility forces one to deny that the phenomena analyzed using counterpart theories are profound. While the extant literature discusses this worry only briefly, I offer novel ways to construe the problem. In particular, counterpart theories undermine metaphysical presuppositions in other discussions, including debates about responsibility or the moral status of embryos. I show that, rather than undermining counterpart theories, this merely forces their defenders to choose between two alternatives: either they argue that this flexibility is in fact a strength and puts the focus in these debates back on what truly matters, or they formulate less flexible versions of counterpart theories. I offer elaborations of both options.