A new algorithm is presented for the calculation of multiphase equilibrium conditions at fixed temperature, pressure, and overall composition. The method enables the simultaneous analysis of phase stability and equilibrium compositions for coexisting phases by the minimization of the Gibbs free energy of the system. The Lagrange multipliers for the test phases, which are provided by the optimization routines utilized, are additional variables indicating the feasibility and potential for the formation of the phases. The approach of this study is illustrated for the phase behavior of several systems.