Since qualitatively indiscernible worlds are no help to Lewis in accounting for haecceitistic possibilities—e.g., where two twins swap their qualitative roles—and Lewis takes these to be genuine possibilities, he offers an important modification to his earlier version of counterpart theory with the aim of explaining how such haecceitistic possibilities are represented. Lewis’ modified counterpart theory permits individuals to have multiple counterparts within the actual world. (See Lewis (1967, 1983, and 1986).) So, in the case of our two twins, the firstborn twin has its second-born twin as one of its counterparts. In certain contexts, the second-born twin therefore represents a possibility for the firstborn—namely, the possibility of occupying precisely the qualitative role of the second-born twin. In this way, the actual world and its parts will, in suitable contexts, represent, not only the actualized maximal possibility, but also maximal possibilities that differ haecceitistically from the actualized maximal possibility. Context permitting, each possible world can therefore represent a plurality of maximal possibilities each of which differ haecceitistically from one another. And, since Lewis’ modified counterpart theory holds a single possible world and its parts to represent distinct maximal possibilities that differ haecceitistically, it accommodates the representation of such possibilities without multiplying possible worlds. Accordingly, Lewis describes it as “haecceitism on the cheap.” Understood in terms set out above, this “cheap substitute for haecceitism” entails Possibility Haecceitism yet rejects World Haecceitism.