We consider an analog of entanglement-swapping for a set of black boxes with the most general nonlocal correlations consistent with relativity (including correlations which are stronger than any attainable in quantum theory). In an attempt to incorporate this phenomenon, we consider expanding the space of objects to include not only correlated boxes, but “couplers,” which are an analog for boxes of measurements with entangled eigenstates in quantum theory. Surprisingly, we find that no couplers exist for two binary-input–binary-output boxes, and hence that there is no analog of entanglement swapping for such boxes.