Nonclassically causal correlations without backwards-in-time signaling

We investigate the relationship between no backwards in time signalling and classically causal correlations. We discover that unlike the case for two parties, the no backwards in time signaling paradigm for three parties is not enough to ensure that correlations can be reproduced with a classical causal ordering. We demonstrate this with an explicit example. We also generalise some existing results for linear two-time states to multi-party scenarios.