Asserting phase stability entails the global solution of a nonconvex optimisation problem, typically the tangent plane distance minimisation (TPDM). To improve computational tractability, we propose classifier-based surrogate models to replace the TPDM. We seek models that represent several multicomponent mixtures simultaneously, across various component identities, temperatures, and compositions. We investigate both artificial neural networks (ANN) and support vector machines (SVM) and use Matthew's correlation coefficient (MCC) as performance metric for the corresponding binary classification problems. For SVM models, linear, polynomial, and radial basis function (RBF) kernels are assessed; while for ANNs, the tanh and relu activation functions are investigated. We test the performance of these surrogate models on a set of ternary mixtures that involve ibuprofen and two solvents with fixed or variable temperatures. The results show that ANNs and SVMs can both predict phase stability reliably, with RBF-SVM giving the lowest computational cost.