The regime of multicascade proton acceleration during the interaction of a $10^{21}-10^{22}$ W/cm$^2$ laser pulse with a structured target is proposed. The regime is based on the electron charge displacement under the action of laser ponderomotive force and on the effect of relativistically induced slab transparency which allows realization of the idea of multicascade acceleration. It is shown that a target comprising several thin foils properly spaced apart can optimize the acceleration process and give at the output a quasi-monoenergetic beam of protons with energies up to hundreds of MeV with an energy spread of just a few percent.