The possibility of a person switching bodies presents a challenge to Lewis's conviction that necessarily, a person occupies a body at a time if and only if that person is identical with that body at that time. In order to meet this challenge, Lewis modifies his counterpart theory to allow for multiple counterpart relations (e.g., one's personal counterpart, one's bodily counterpart). The wider significance of this modification lies in the general scheme it offers for translating any modal predication in which referential transparency fails (because the sense of the subject term is used in a way that extends beyond a determination of its denotation) into sentences of counterpart theory with multiple counterpart relations.