We examine the effects of medium dependence of the two-body dynamics on the many-body properties of Fermion systems, with approximation ultimately aimed at lower densities for all temperatures. The dynamics are initially treated in terms of a pair-composite formulation given previously, and the underlying single-Fermion nature of the pair constituents allows interpretation via more conventional thermal many-body formalism. This permits construction of coupled equations for composite amplitudes and bound states, single-particle energy
and momentum distributions, and macroscopic thermodynamic properties. We explore differences between our results and those of traditional theories which incorporate two-body correlations in some fashion, and we display explicitly how correct limiting results are recovered from our equations when the density and/or coupling strength is decreased. Finally, we provide an interpretation of our results via a form of quasiparticle quantum cluster expansion analogous to the familiar particle quantum cluster expansion.