Multi-principal-element alloys (MPEAs) are a wide class of materials currently at the center of numerous investigations. Key-issues with MPEAs are related with controlling the onset of (i) long-range order and (ii) phase separation, both processes being in general detrimental to the properties. While trends (i) and (ii) are strongly dependent on the precise proportions of metallic elements around the reference equiatomic MPEA, the tremendously large composition space makes it a tricky task to heuristically identify optimized MPEAs. In practice, this often leads to undesired second-phase ordered particles. This deficiency emphasizes the relevance of modelling and simulation tools designed to facilitate the exploration of MPEA composition spaces. In this atomic-scale work, we propose a “composition-constrained” point mean-field formalism resting on alloy pair energetics, to investigate trends (i) and (ii). This formalism is currently applicable to a wide panel of such systems built from ~ 30 chemical elements. Its application to several MPEAs along the AlCoCrFeNi → AlCrFeMnNi → AlCrFeMnMo sequence evidences striking differences between these systems, and demonstrates its efficiency to get at-a-glance information about (i) and (ii) features for various MPEAs. The flexibility of the proposed simulation approach makes it easily employable in conjunction with experiments on well-equilibrated MPEA samples, for thermodynamic characterizations of MPEAs.