All that said, the counterpart theory admits of various modifications and developments—beside translation schemes alternative to Lewis’s one, several changes to the framework, more or less departing from the original intent of the theory, have been subsequently proposed (see Forbes (1982, 1983, 1987, 1990), Ramachandran (1989, 1990, 1998, 2003, 2008) for much discussion), and various systems have been constructed incorporating at least some aspects of the counterpart theory (see overviews, proposals and further references in Corsi (2002, 2003), Kracht and Kutz (2002, 2005, 2007), Belardinelli (2006, 2007), Brauner and Ghilardi (2006)). Lewis himself was also ready to contemplate various amendments, as well as to change properties codified in the list of axioms quoted above. Thus, instead of single counterpart relation, Lewis (1971) introduces multiple such relations:
... counterpart relations are a matter of over-all resemblance in a variety of respects. If we vary the relative importances of different respects of similarity and dissimilarity, we will get different counterpart relations. Two respects of similarity or dissimilarity among enduring things are, first, personhood and personal traits, and, second, bodyhood and bodily traits. If we assign great weight to the former, we get the personal counterpart relation. Only a person, or something very like a person, can resemble a person in respect of personhood and personal traits enough to be his personal counterpart. But if we assign great weight to the latter, we get the bodily counterpart relation. (Lewis 1971: 208)
Figure 3.1: Multiple counterpart relations in a counterpart model
Semantics with multiple counterpart relations allows one to consider an object from different perspectives, making available attribution of different modal properties via distinct counterpart relations, tracking the very same object along different modal paths (and thus admitting a possibility that the very same object may be represented by a counterpart, determined by a counterpart relation C1, such that it is assigned a property P at another world, and another counterpart— determined by C2—such that it lacks P at the same world).