The quantum theory of renormalized energy spectrum of the system of localized two-level quasiparticle, with degenerated spectrum, interacting with polarization phonons, being the model of multilayered nanostructure, is developed within the modified Feynman-Pines diagram technique. Effectively taking into account the multi-phonon processes, the theory is valid in a wide range of energies which contains the main states and the satellite groups of energies produced by the resonant bound-to-phonons states of quasiparticle in the vicinity of the threshold energies of their radiation. The properties of renormalized spectrum of the system are analyzed and dependences of the widths of groups of energy levels (main and satellite) on the magnitudes of inter-level coupling constants are obtained.