the work of bancal et al. generalizes bell’s result by proving that correlations achievable in quantum theory are also incompatible with a large class of superluminal hidden variable models. in this framework, faster-than-light signaling is precluded. however, the choice of settings of one party can influence hidden variables at another party’s distant location, if there is enough time for a superluminal influence (of finite, but otherwise unknown speed) to propagate from one point to the other. in this scenario, any bipartite experiment revealing bell nonlocality can just provide lower bounds on the hidden influence’s propagation speed. quantum experiments with three or more parties can, nonetheless, disprove all such non-local hidden variable models.