The parallel implementation of MUPHY, a concurrent multiscale code for large-scale hemodynamic simulations in anatomically realistic geometries, for multi-GPU platforms is presented. Performance tests show excellent results, with a nearly linear parallel speed-up on up to 32GPUs and a more than tenfold GPU/CPU acceleration, all across the range of GPUs. The basic MUPHY scheme combines a hydrokinetic (Lattice Boltzmann) representation of the blood plasma, with a Particle Dynamics treatment of suspended biological bodies, such as red blood cells. To the best of our knowledge, this represents the first effort in the direction of laying down general design principles for multiscale/physics parallel Particle Dynamics applications in non-ideal geometries. This configures the present multi-GPU version of MUPHY as one of the first examples of a high-performance parallel code for multiscale/physics biofluidic applications in realistically complex geometries.