Copper(II)-nitroxide based Cu(hfac)2LR compounds exhibit unusual magnetic behavior that can be induced by various stimuli. In many aspects, the magnetic phenomena observed in Cu(hfac)2LR are similar to classical spin-crossover behavior. However, these phenomena originate from polynuclear exchange-coupled spin clusters Cu2+-O˙-N< or >N-˙O-Cu2+-O˙-N<. Such peculiarities may result in additional multifunctionality of Cu(hfac)2LR compounds, making them promising materials for spintronic applications. Herein, we investigate the Cu(hfac)2LMeMe material, which demonstrates a three-step temperature-induced magnetostructural transition between high-temperature, low-temperature, and intermediate states, as revealed by magnetometry. Two main steps were resolved using variable-temperature Fourier-transform infrared and Q-band electron paramagnetic resonance (EPR) spectroscopies. The intermediate-temperature states (∼40-90 K) are characterized by the coexistence of two types of copper(II)-nitroxide clusters, corresponding to the low-temperature and high-temperature phases. High-field EPR experiments revealed the effect of partial alignment of Cu(hfac)2LMeMe microcrystals in a strong (>20 T) magnetic field. This effect was used to unveil the structural features of the low-temperature phase of Cu(hfac)2LMeMe, which were inaccessible using single-crystal X-ray diffraction (XRD) technique. In particular, high-field EPR allowed us to determine the relative direction of the Jahn-Teller axes in CuO6 and CuO4N2 units.