A two-phase numerical process is proposed for gradient-based multidisciplinary optimization. In a first phase, one or several Pareto-optimal solutions associated with a subset of the cost functions, the primary objective functions, subject to constraints, are determined by some effective multi-objective optimizer. In the second phase, a continuum of Nash equilibria is constructed tangent to the Primary Pareto Front along which secondary cost functions are to be reduced, while best preserving the Pareto-optimality of the primary cost functions. The focus of the article is on estimating the rate at which the secondary cost functions are diminished. The method is illustrated by the numerical treatment of the optimal sizing problem of a sandwich panel w.r.t. structural resistance under bending loads and blast mitigation.