Boosts in an arbitrary direction and maximal causal velocities in a   deformed Minkowski space
  We discuss boosts in a deformed Minkowski space, i.e. a four-dimensional space-time with metric coefficients depending on non-metric coordinates (in particular on the energy). The general form of a boost in an arbitrary direction is derived in the case of space anisotropy. Two maximal 3-vector velocities are mathematically possible, an isotropic and an anisotropic one. However, only the anisotropic velocity has physical meaning, being invariant indeed under deformed boosts. 
Fabio Cardone, Alessio Marrani and Roberto Mignani