An emerging motor type, the variable flux permanent magnet (VFPM) motor, has created a demand for permanent magnets with a new set of properties. These magnets must exhibit easily tunable magnetization, demanding for moderate coercivity values, low magnetizing fields, and first-order reversal curves (FORCs) with high flatness. In this work, we report that the doping of Sm and La in Nd-Fe-B-based hot-deformed magnet, followed by the Nd-Cu diffusion process, resulted in desirable magnetic properties, such as, a moderate coercivity (µ0Hc) of 0.55 T, a low magnetizing field (µ0Hmag) of 0.94 T and a high FORC flatness of 0.96, while maintaining a high remanence (µ0Mr) of 1.3 T. The FORC flatness achieved in this work is the highest and the comprehensive properties are superior to the previously reported Nd-Fe-B magnets for VFPM motors. Microscopic investigations revealed that the high flatness achieved in this hot-deformed magnet is attributed to the formation of Fe-lean thick intergranular phases realized by Nd-Cu grain boundary diffusion. The overall combination of the magnetic properties for the diffusion processed (Nd,Sm,La)-Fe-B magnet is excellent, in comparison with a commercially available Sm2Co17-type magnet, showing the promise of the former for use in VFPM motors.