Stability is a crucial issue to consider for control system design. In this paper a new multi-objective approach to approximate the stabilizing region for linear control systems is proposed. The design method comprises two stages. In the first stage, a bi-objective sub-problem is solved: the algorithm aims to calculate the vertices that maximize both the volume of the decision space and the percent of stable individuals generated within the decision space. In the second stage, the information gathered during the first stage is used to solve the actual multi-objective control design problem. To evaluate the proposed method a PID design problem is considered. Results show that in this case, our method is able to find better Pareto approximations than the classical approach.