The effect of the partial substitution of Fe by Co and Mn on the structural and magnetic properties of Fe-Pd alloys has been investigated by means of calorimetric, magnetic and neutron diffraction measurements. The addition of Mn increases both the reversible and irreversible MT temperatures whereas the addition of Co causes the opposite effect, which points out that that the compositional dependence of the transformation temperatures of the Fe-Pd alloys is not related to the Pd amount but to the e/a concentration. Furthermore, it is shown that the appearance of the BCT phase is directly related to the tetragonality of the FCT phase. On the other hand, the amount of FCT martensite that irreversibly transforms into the undesirable BCT phase is considerably reduced by both the Co and Mn doping. The substitution of Fe by Co seems to be especially interesting for magnetic field-induce strains applications since both the magnetic anisotropy and the saturation magnetization of the Fe-Pd FCT martensite are considerably increased with the Co addition.