The generalized Dyson boson mapping is extended to multifermion systems containing three- particle substructures as occuring in nuclear matter. Two different approaches are described. The first one leads to a mapping involving equal numbers of bosons and fermions, where each boson, as usual, represents a fermion pair. The second possibility consists of the introduction of new kinds of fermions carrying the quantum numbers of the original three-fermion subsystems. Both transformations are nonunitary.