In this study, the modified bounded homotopies presented by Malinen and Tanskanen (Malinen, I.; Tanskanen, J. Modified bounded homotopies to enable a narrow bounding zone. Chem. Eng. Sci. 2008, 63, 3419) are investigated in order to solve phase stability analysis problems in liquid liquid equilibrium cases for phase-splitting calculations. The tangent-plane distance criterion is used to analyze the phase stability. The emphasis is on approaching the first root on the homotopy path. According to the observations, the bounding of the homotopy path with respect to the problem variables aids in the solving of a phase stability analysis problem. The main shortcomings of the modified bounded Newton, affine, and fixed-point homotopies are the starting point isolas, the existence of unfeasible solutions, and the convergence to only certain roots, respectively. The attraction domain of the global minimum was observed to be the largest with the fixed-point homotopy. Sequential usage of the fixed-point homotopy and starting points near pure components results in a robust algorithm for phase stability analysis and gives feasible initial estimates for the solving of phase splitting.