  We extend our recent results on ordinary su(N) tensor product multiplicities
to higher su(N) tensor products. Particular emphasis is put on four-point
couplings where the tensor product of four highest weight modules is
considered. The number of times the singlet occurs in the decomposition is the
associated multiplicity. In this framework, ordinary tensor products correspond
to three-point couplings. As in that case, the four-point multiplicity may be
expressed explicitly as a multiple sum measuring the discretised volume of a
convex polytope. This description extends to higher-point couplings as well. We
also address the problem of determining when a higher-point coupling exists,
i.e., when the associated multiplicity is non-vanishing. The solution is a set
of inequalities in the Dynkin labels.
