The spin Peltier effect (SPE), heat-current generation as a result of spin-current injection, has been investigated in alternately stacked Pt/${\mathrm{Fe}}_{3}{\mathrm{O}}_{4}$ multilayer films. The temperature modulation induced by the SPE in the $[\text{Pt}/{\mathrm{Fe}}_{3}{\mathrm{O}}_{4}]\ifmmode\times\else\texttimes\fi{}n$ films was found to be significantly enhanced with increasing the number of Pt/${\mathrm{Fe}}_{3}{\mathrm{O}}_{4}$ bilayers $n$. This SPE enhancement is much greater than that expected for a simple stack of independent Pt/${\mathrm{Fe}}_{3}{\mathrm{O}}_{4}$ bilayers. The observed $n$ dependence of the SPE can be explained by introducing spin-current redistribution in the multilayer films in the thickness direction, in a manner similar to the enhancement of the spin Seebeck effect in multilayers.