The core is one of the most widely used cooperative solution concepts in applications to the social sciences, providing a rigorous formulation of Edgeworth's original insight on the stability of surplus allocation. By requiring that no coalition can "block" a proposed allocation, the standard definition of the core implicitly allows blocking coalitions to coordinate on arbitrary distributions of their joint payoff, tailored to the allocation under consideration. We question whether this degree of flexibility adequately reflects the notion of a credible blocking agreement. In response, we require that admissible blocking agreementsbe consistent, in the sense that they coincide with the expected outcome of the subgame that arises when the members of a blocking coalition leave the grand coalition. Naturally, these outcomes are independent of the allocation being challenged. The resulting solution concept is a superset of the core, providing a solution in practically relevant applications where the core is empty. Specifically, we show that it is non- empty for all symmetric, superadditive transferable utility games satisfying a convexity condition, as well as for all three-player superadditive games. From an economic perspective, our solution captures the possibility of collusion among players in a competitive scenario, and the influence of non-contributing players on the outcome.