The structural and concentration changes in a multilayer Ni(25 nm)/Cu(25 nm)/Cr(25 nm) nanosystem on a single-crystal Si(100) substrate are studied under heat treatment in oxygen-containing and neutral atmospheres at temperature of 450°C, as well as under additional ion (Ar$^{+}$) irradiation with an energy of 800 eV and a fluence of 5.6$\cdot10^{16}$ ion/cm$^2$. The influence of various initial defect structures of the samples on i) the effect of dimensional instability, which appears in the formation of micropores, ii) the concentration changes, including saturation with impurities, as well as iii) the mechanisms and regularities of diffusion processes, are analysed. For this purpose, synchrotron radiation at the BL44B2 RIKEN Material Science Beamline of the SPring-8 Centre, Auger electron spectroscopy (Jamp-9500F, Jeol), and scanning electron microscopy are used. As observed, upon conditions of heat treatment in an argon atmosphere, the film’s initial structure does not affect the defects evolution and diffusion processes behaviour. At the same time, annealing in argon accelerates Ni bulk diffusion into the Cu layer and grain boundary diffusion of Cu into the Ni layer compared to annealing in a vacuum of 10$^{-3}$ Pa. After vacuum annealing of films with nanosized pores in the initial state, not only intense diffusion of Cr towards the outer surface is observed (the concentration of Cr in the near-surface layer reaches $\cong$ 25 at.%) with its subsequent oxidation, but also catastrophic saturation of the Cr layer with carbon—up to 30 at.%. The preliminary ion surface treatment reduced the amount of carbon significantly and increased the Cu crystalline structure’s perfection.