In this talk, we will be concerned with the existence of a third embedded minimal hypersurface spanning a closed submanifold B contained in the boundary of a compact Riemannian manifold with convex boundary, when it is known a priori the existence of two strictly stable minimal hypersurfaces that bound B. In order to do so, we develop min-max methods similar to those of the recent work of De Lellis and Ramic, adapted to the discrete setting of Almgren and Pitts.