All 32 elements of the quiescent and modulation components M and DeltaM of the Mueller matrix M that describes the elastic scattering of light from a depolarizing sample subjected to time-harmonic modulation of frequency Omega can be simultaneously retrieved from the spectrally separated baseband and modulated-carrier components of a single detected signal by using a photopolarimeter whose polarizing and analyzing optics are modulated at lower frequencies omegak << Omega. Some of the prospective applications of this powerful technique of modulated-Mueller-matrix photopolarimetry (MMMP) are indicated.