[en] The structure of multiphonon K = 4 γγ-band of ${}^{112}\mathrm{R}\mathrm{u}$, ${}^{104}\mathrm{M}\mathrm{o}$, ${}^{106}\mathrm{M}\mathrm{o}$ , and ${}^{108}\mathrm{M}\mathrm{o}$ nuclei are investigated using the recently proposed modified soft rotor formula (MSRF). The positive values of the moment of inertia and small values of softness parameter are obtained. The calculated values of moment of inertia of γγ-band are almost equal to the moment of inertia of γ-band, which indeed should be equal to the moment of inertia of ground band. The constant energy parameter EK in the MSRF is also illustrated for K = 4 γγ-band. The staggering pattern in the multiphonon γγ-band is also discussed in detail. The study of one-phonon K = 2 γ-band and two-phonon K = 4 γγ-band using MSRF yields good energy values. (paper)