Abstract: We consider semimultiplicative sets. These are sets with a partially defined associative multiplication. They naturally generalize groups, groupoids, semigroups and small categories. One can associate reduced $C^*$-algebras and crossed products to them. For instance, Toeplitz-Cuntz-Krieger algebras of higher rank graphs can be realized as the reduced $C^*$-algebra of the path space of the underlying graph. We are interested in the $K$-theory of such $C^*$-algebras and propose a semimultiplicative set equivariant $KK$-theory, which generalizes Kasparov's equivariant $KK$-theory for groups, as a possible tool to tackle such $K$-theory computations.