  Coincidence Site Lattices (CSLs) are a well established tool in the theory of
grain boundaries. For several lattices up to dimension $d=4$, the CSLs are
known explicitly as well as their indices and multiplicity functions. Many of
them share a particular property: their multiplicity functions are
multiplicative. We show how multiplicativity is connected to certain
decompositions of CSLs and the corresponding coincidence rotations and present
some criteria for multiplicativity. In general, however, multiplicativity is
violated, while supermultiplicativity still holds.
