We show how a proper radial modulation of the composition of core-multi-shell nanowires (NWs) critically enhances the control of the free-carrier density in the high-mobility core with respect to core-single-shell structures, thus overcoming the technological difficulty of fine tuning the remote doping density. We calculate the electron population of the different NW layers as a function of the doping density and of several geometrical parameters by means of a self-consistent Schrödinger-Poisson approach: free carriers tend to localize in the outer shell and screen the core from the electric field of the dopants.