The interest in high entropy alloys and other metallic compounds with four or more elements at near-equiatomic ratios has drawn attention to the ability to rapidly predict phase behavior of these complex materials, particularly where existing thermodynamic data are lacking. This paper discusses aspects of this from the point of view of predicting without utilizing (or fitting) experimental data. Of particular interest are heuristic approaches that provide prediction of single-phase compositions, more rigorous approaches that tackle the thermodynamics from a more fundamental point of view, and simulation approaches that provide further insight into the behaviors. This paper covers cases of all three of these, in order to examine the strengths and weaknesses of each approach, and to indicate directions where these may be utilized and improved upon. Of particular interest is moving beyond “which composition may form a solid solution,” to recognizing the importance of underlying thermodynamic realities that affect the temperature- and composition-dependent transformations of these materials.