If magnetic semiconductors are ever to find wide application in real spintronic devices, their magnetic and electronic properties will require tailoring in much the same way that bandgaps are engineered in conventional semiconductors. Unfortunately, no systematic understanding yet exists of how, or even whether, properties such as Curie temperatures and bandgaps are related in magnetic semiconductors. Here we explore theoretically these and other relationships within 64 members of a single materials class, the Mn-doped II-IV-V-2 chalcopyrites (where II, IV and V represent elements from groups II, IV and V, respectively); three of these compounds are already known experimentally to be ferromagnetic semiconductors. Our first-principles results reveal a variation of magnetic properties across different materials that cannot be explained by either of the two dominant models of ferromagnetism in semiconductors. On the basis of our results for structural, electronic and magnetic properties, we identify a small number of new stable chalcopyrites with excellent prospects for ferromagnetism.