 Given No gaps plus No overlaps, further equivalences follow. On the monistic side, the two conjuncts of Priority monism (cosmic)—\(\exists !xBx\) and \(Bu\)—turn out to be mutually entailing. And likewise on the pluralistic side, the two conjuncts of Priority pluralism (partial)—\(\exists x\exists y(Bx \amp By \amp x\ne y)\) and \({\sim}Bu\)—turn out to be mutually entailing. That is to say that, given the tiling constraint, the numerical thesis that the number of basic concreta is one turns out equivalent to the holistic thesis that the basic concretum is mereologically maximal.