New physical effects take place when the phase velocity of a moving isotropic medium is above the speed of light in vacuum (superluminal regime), namely: i) complex aberration, i.e., complex angles in the proper frame actually correspond to real angles in the lab frame; ii) a new Cerenkov region, where the phase velocity is below the relative velocity between frames. In fact, by considering lossless zero refractive index metamaterials, these effects can still occur for non-relativistic velocities. However, when losses are taken into account, these effects can only be obtained for relativistic velocities. In this communication we address the superluminal regime for moving bi-isotropic media. As these media can be studied as a superposition of two moving isotropic media, a new combination of the effects that are usually found for the superluminal and subluminal regimes can occur. Furthermore, the influence of the new degrees of freedom on the “slow” relativistic effects is studied. These media are then analyzed through the Bohren decomposition using spacetime algebra (the geometric algebra of Minkowski spacetime). This new approach circumvents the cumbersome calculations that are usually associated with this problem.