For a system of indistinguishable fermions with pairwise interactions, we consider renormalized, perturba-tive expansions for the three-and four-particle propagators Green's functions in terms of exact one-particle propagators, along with a pair interaction that may be bare as it appears in the Hamiltonian or dressed polarized. Care is taken to provide a rigorous foundation for the diagrammatic representations of these perturbation series; in particular, it is demonstrated how each topologically distinct diagram represents an embedding in three-dimensional space of numerous separate terms in the perturbation series. Within a renor-malized ladder approximation for the three-and four-particle propagators, we derive diagram weights which differ from the two-particle diagram weights in order to limit the perturbation series to topologically distinct, permutationally independent diagrams. These results lay the foundation for perturbative approximations that decouple the propagator and density matrix equations of motion.