"x > c" is a binary test, BTW.
Part of the point of experimentation is to find holes in our existing models, so it is reasonable for scientists to look for faster than C without violation of causality.
As an example, suppose that we were able to go faster than C in the reference frame of the fixed distant stars, but not in other reference frames. There are reference frames where you can go backwards in time, but none in which you can violate causality.
(That said, General Relativity allows for causality violations. However setting them up is well beyond any engineering ability our species is likely to develop...)
Of course I state this as a theoretical point only - there is absolutely no reason to suspect that any such thing is possible.