  Causal order -- an essential part of our conception of time and the natural
world -- is challenged by general relativity and quantum gravity. This
discrepancy asks for physical principles to reject violations of causal order
as mathematical artifacts, or to revisit our conception of the world. Recent
studies target this discrepancy and unveil the compatibility of violations of
causal order with various natural desiderata: logical consistency, linear and
reversible dynamics, computational tameness, and quantum-to-classical
transitions. Here, we present causal-order violating processes among arbitrary
many regions, where each region influences every other but itself: The above
desiderata are altogether insufficient even to limit the degree of
"acausality." Our results exhibit qualitative and quantitative parallels with
the Ardehali-Svetlichny non-local game.
