I was trying to think in general means to localy preserve causality. By "means", it means to include (or not) varying speed of light and faster than light sign propagation. By varying speed of light, it means that light speed can localy depend on the most generical parameters you can get. Don't think in terms of special relativity and space time, just any general cases 3 and 4 manifolds. Go as crazy as you can get, as long as you are mathematicly consistent. Don't worry about trying to get realistic physics right now.