Designing optimal linear systems has extended the traditional optimization method (i.e. finding an optimal point for a given system) to finding an optimal solution structure. This structure consists of optimal systems and their optimal contingency plans which can cope with various decision situations under uncertainty. Multi-criteria and multi-constraint-levels (MC²) simplex method is a primary tool used in designing optimal systems. In this paper, a new approach to designing optimal systems is proposed to find dual flexible contingency plans (DFCP) for generalized good systems (GGS). GGS goes beyond the assumption of selecting opportunities for a potentially good system, while DFCP utilizes all possible slack resources and converts non-optimal solutions into optimal ones. This approach enriches the theoretical framework of designing optimal systems. A numerical example is used to illustrate the proposed approach.