  By studying generalized non-signalling theories, the hope is to find out what
makes quantum mechanics so special. In the present paper, we revisit the
paradigmatic model of non-signalling boxes and introduce the concept of a
genuine box. This will allow us to present the first generalized non-signalling
model featuring quantum-like dynamics. In particular, we present the coupler, a
device enabling non-locality swapping, the analogue of quantum entanglement
swapping, as well as teleportation. Remarkably, part of the boundary between
quantum and post-quantum correlations emerges in our study.
