Information on the energy, charge, and spin characteristics of Pd$_{1-x}Me_{x}$MnSn ($Me$ = Co, Ni, $x$ = 0.0–1.0) is obtained using band calculations within the FLAPW (full-potential linearized augmented-plane-wave) model. As determined, an increase in the concentration of the cobalt or nickel atoms leads to an increase in the interatomic electron density inside the alloys. This results in both a concurrent reduction in the parameters of their crystal lattices and an increase in the binding energies of the atoms. The number of electrons $Q$ within the atomic spheres of Pd, Mn, and Sn in cobalt-containing alloys exceeds the corresponding values for nickel-containing phases, and the dependences of $Q$ exhibit a systematic tendency to increase with the growth of substitutional-atoms’ concentrations. The observed polarization of valence electrons leads to the appearance of magnetic moments on the atoms of the alloys. The magnetic moments of metal atoms are ferromagnetically ordered, and their magnitude depends on the type and concentration of substitutional atoms.