Although explicit in time algorithms for low-dissipation high-order methods are very computationally efficient when employed in the context of LES and DNS for compressible flows, their conditional stability properties can lead to severe restrictions on the time step size, or even to the impossibility of performing the simulation due to early divergence in results. On the other hand, fully implicit methods are complex to implement, and often have issues dealing with the non-linear convective terms of the Navier-Stokes equations, especially when shocks develop in the flow. This work combines the SEM-ENVIT model previously presented in [1] and implemented in the SOD2D code [2] with a semi-implicit scheme of the IMEXRK family of temporal integration algorithms in an effort to provide a stable, high-accuracy model for compressible LES and DNS simulations.