We demonstrate by means of fully relativistic first principles calculations that, by substitution of Fe by Cr, Mn, Co, Ni or Cu in FePt-L10 bulk alloys, with fixed Pt content, it is possible to tune the magnetocrystalline anisotropy energy by adjusting the content of the non-magnetic species in the material. The changes in the geometry due to the inclusion of each element induces different values of the tetragonality and hence changes in the magnetic anisotropy and in the net magnetic moment. The site resolved magnetic moments of Fe increase with the X content whilst those of Pt and X are simultaneously reduced. The calculations are in good quantitative agreement with experimental data and demonstrate that models with fixed band structure but varying numbers of electrons per unit cell are insufficient to describe the experimental data for doped FePt-L10 alloys.