In L10 (fct)-FePt thin films, both tuning Fe and Pt concentrations and substitution with third-metal were studied for magnetic characteristic optimization. We investigated single-crystalline FePt-X (X = Mn, Ni, Cu) thin films grown epitaxially on MgO(001) substrates at a substrate temperature of 350°C by changing Fe, Pt, and X contents, and explored the effects of off-stoichiometry and 3d-metal-substitution. The magnetic moment per atom (m) of FePt-X films as a function of the effective number of valence electrons (neff) in 3d metal sites follows the Slater-Pauling-type trend, by which m decreases by the neff deviation from neff = 8, independently of the X metal and the Pt concentration. The magnetic anisotropy (Ku) exhibits neff dependence similar to m. This trend was almost independent of the Pt concentration after compensation using the theoretical prediction on the relation between Ku and Fe/Pt concentrations. Such a trend has been proved for stoichiometric FePt-X films, but it was clarified as robust against off-stoichiometry. The compensated Ku (K u comp) of FePt-Mn and FePt-Cu followed a similar trend to that predicted by the rigid-band model, although the K u comp of the FePt-Mn thin films dropped more rapidly than the rigid band calculation. However, it followed the recent first-principles calculation.