The multi-scale zero relaxation singular limit for gas dynamics in thermal non-equilibrium with multiple non-equilibrium modes in multi-dimensions with physical boundaries from non-equilibrium to thermal equilibrium of compressible Euler flow is proved in this paper for analytical data by establishing the uniform local-in-time estimates. A cancellation mechanism is utilized to deal with the nonlinear singular terms that cause the increase in both time and space derivatives in energy estimates. The rates of the relaxations corresponding to different non-equilibrium modes tending to zero discussed in this paper can be arbitrarily different.