The vastness of the space of possible multicomponent metal alloys is hoped to provide improved structural materials but also challenges traditional, low-throughput materials design efforts. Computational screening could narrow this search space if models for materials stability and desired properties exist that are sufficiently inexpensive and accurate to efficiently guide experiments. Toward this effort, here we develop a method to rapidly assess the thermodynamic stability of a metal alloy composition of an arbitrary number of elements, stoichiometry, and temperature based on density functional theory (DFT) data. In our model, the Gibbs free energy of the solid solution contains binary enthalpy contributions and ideal configurational entropy, whereas only enthalpy is considered for intermetallic competing phases. Compared to a past model for predicting the formation of single-phase high-entropy alloys [M. C. Troparevsky et al., Phys. Rev. X 5, 011041 (2015)], our method is similarly inexpensive, since it assesses enthalpies based on existing DFT data, but less heuristic, more broadly applicable, and more accurate (70%–75%) compared to experiment.