Molecular solids like sodium superoxide NaO2 exhibit intricate magnetic behavior despite their simple chemical structure. This is due to the interplay of spin, orbital and lattice degrees of freedom which leads to intriguing effects related to reorientation of O2-molecular p orbitals. Multiple magnetic regimes were indeed observed in NaO2 in our previous NMR and muSR studies. Among other surprising findings is the discovery of a field-induced magnetic phase below 3 K if the applied magnetic field exceeds about 100 G. Here we propose to carry on the muSR investigation of the field-induced phase down to the lowest experimentally accessible temperatures. We expect that these measurements at temperatures where temperature fluctuations are minimized will provide invaluable information about the mechanism of the observed field-induced effect.