This paper argues that counterpart-theoretic accounts of modality that allow for many-one counterpart relations, and thereby make room for contingent identities, are not able to preserve the transitivity of identity. It will be shown that the translation scheme of counterpart theorists breaks down and that they have to abandon the claim that objects can be contingently identical in virtue of sharing a counterpart. Moreover, modifications of counterpart theory that preserve the transitivity of identity are shown to require jettisoning the idea that the counterpart relation is a similarity relation and greatly reduce the explanatory power of counterpart theory.