Topology optimization can be formulated with constraints on the interface stiffness matrix. This yields a load-independent alternative to classical displacement or compliance constraints [1]. In the MK-problem, the structural mass of a component with n interfaces is minimized subject to the semidefinite requirement K-K_c≥0, where K is the condensed interface stiffness matrix and K_c is a prescribed lower bound. Previous studies have demonstrated the potential of this formulation for two-interface components [1,2]. However, enforcing the matrix inequality directly via eigenvalue constraints can suffer from poor convergence when eigenvalues become repeated, i.e., when multiple critical modes approach zero simultaneously [1,4]. This work makes two contributions. First, we extend the MK formulation to components with an arbitrary number of interfaces using static condensation to rigid interface degrees of freedom, yielding an interface stiffness matrix that captures both the individual interface stiffnesses and their mutual coupling. Second, we introduce a robust approximation based on a sequence of substitutive problems. The semidefinite constraint is replaced by a finite, adaptively generated set of generalized compliance constraints of the form l_k≤l_c. Each constraint corresponds to an interface load case derived from the most critical directions of the stiffness deficit of D=K-K_c. For each load case, a standard compliance-constrained topology optimization problem is solved reliably using state-of-the-art methods [3]. A two-dimensional benchmark with three interfaces demonstrates improved robustness over direct eigenvalue-constrained formulations while preserving the load independence and system-level interpretability of the MK-problem.