We present a study of the mixing energies and the effective cluster interactions which form the configurational part of the internal energy of Pd-Rh substitutional alloys. We discuss the tendency towards phase-separation and more generally phase stability. The effects of a substitutional ternary addition on the tendencies toward order or phase-separation are also reported. The Korringa-Kohn-Rostoker Coherent-Potential Approximation (KKR-CPA) is used to investigate the electronic structure effects and energetics of the random alloy. Moreover, we use the Generalized Perturbation Method (GPM), using the KKR-CPA random alloy as a reference medium, to investigate the effective interactions which determine phase stability. We briefly comment on other factors which may give important contributions to the total free-energy of the alloy. We also contrast the GPM with the Connolly-Williams approach for calculating phase diagrams from first-principles. Finally, we explore the inadequacies of the frozen-potential and Harris approximations to the energetics of alloying.