This article provides a brief review of the model referred to as Step Potentials for Equilibria and Discontinuous Molecular Dynamics (SPEADMD) with observations that may be instructive in formulating the next generation of SAFT models. Effects of branches, fused spheres, rings, and molecular flexibility are demonstrated. The evolution of contributions of the equation of state from low to high molecular weight is shown to be sensitive to details of the molecular structure. Statistical mechanical details are shown to affect the formulation of fundamental theory and trends to be expected. Recent results for contributions beyond second order in temperature are shown to substantially improve predictions in the critical region. For mixtures, it is shown how molecular simulation of the off-lattice excess entropy and energy can be achieved, with implications for mixing rules. A heightened emphasis is placed on the confounded nature of molecular scale site site interactions relative to macroscopic pure component and mixture data. This leads to general conclusions about how SAFT models should be articulated going forward, and how progress of the thermodynamic modeling community in general might be improved. (C) 2015 Elsevier B.V. All rights reserved.