The paper introduces a novel approach to the solution of the phase stability problem under constant temperature and pressure with equations of state (EoSs) as the thermodynamic model. An effective strategy that is designed to consecutively transform the tangent-plane distance function (hyper)surface and guarantees a nomepetitive determination of all its stationary points is interwoven within the method's paradigm. The performance profile, efficiency, and effectiveness of the method are illustrated on fifteen systems, which comprise as many as 12 components and are at a wide range of temperature and pressure conditions. The new approach is a first step toward the development of a general solver that can be used with a complete guarantee not only in phase equilibria modeling and calculations but in problems requiring the determination of all minima (maxima) of multimodal functions as well.