Controlling the physical properties of solid forms for active pharmaceutical ingredients (APIs) through cocrystallization is an important part of drug product development. However, it is difficult to know a priori which coformers will form cocrystals with a given API, and the current state-of-the-art for cocrystal discovery involves an expensive, time-consuming, and, at the early stages of pharmaceutical development, API material-limited experimental screen. We propose a systematic, high-throughput computational approach primarily aimed at identifying API/coformer pairs that are unlikely to lead to experimentally observable cocrystals and can therefore be eliminated with only a brief experimental check, from any experimental investigation. On the basis of a well-established crystal structure prediction (CSP) methodology, the proposed approach derives its efficiency by not requiring any expensive quantum mechanical calculations beyond those already performed for the CSP investigation of the neat API itself. The approach and assumptions are tested through a computational investigation on 30 potential 1:1 multicomponent systems (cocrystals and solvate) involving 3 active pharmaceutical ingredients and 9 coformers and one solvent. This is complemented with a detailed experimental investigation of all 30 pairs, which led to the discovery of five new cocrystals (three API−coformer combinations, a polymorphic cocrystal example, and one with different stoichiometries) and a cis-aconitic acid polymorph. The computational approach indicates that, for some APIs, a significant proportion of all potential API/coformer pairs could be investigated with only a brief experimental check, thereby saving considerable experimental effort.