The dependence of the magnetic and photocatalytic properties of the ferrites of Co$_x$Ni$_y$Zn$_{1-x-y}$Fe$_2$O$_4$ composition (where 0 < $x$ < 1 and 0 < $y$ < 1) is considered. The ferrites are synthesized by the plasma method in the form of nanoparticles. A study of the nanoferrites properties of is performed using X-ray phase analysis, vibration magnetometry, and spectroscopy. Photocatalytic properties in the decomposition reaction of methylene blue are determined by UV-spectrograms. Mathematical equations of the dependences of the response functions on the composition are obtained using the simplex method. As found, the saturation magnetization decreases for ferrites of Ni$_{1-x}$Zn$_x$Fe$_2$O$_4$ and Co$_{1-x}$Fe$_2$O$_4$ compositions with increasing zinc cation content. For a number of Ni$_{1-x}$Co$_x$Fe$_2$O$_4$ ferrites, increased magnetic characteristics are observed. The study of catalytic activity against the decomposition reaction of methylene blue shows high photocatalytic properties for double and triple ferrites. A correlation between the photocatalytic activity and the band gap energy is determined.