Multiphase machines are a promising alternative for high-reliability applications. In these applications, overmodulation (OVM) is important since it allows attaining higher modulation indices by injecting, besides zero-sequence voltage harmonics, current-producing ones. In general, the existing techniques are able to limit to some extent the current total harmonic distortion (THD). However, most do not ensure the minimum current THD, thereby not guaranteeing the minimum harmonic stator copper loss. Furthermore, most are intended just for particular phase numbers n, symmetrical/asymmetrical winding arrangements and neutral-point (NP) configurations. OVM with low THD remains unaddressed in most types of multiphase motors. This paper overcomes these limitations by proposing a generalized OVM strategy that attains the minimum current THD in induction motors with any n, winding arrangement and NP configurations. Two techniques are outlined. One of them injects only non-torque-related harmonics, while the other technique exploits torque-producing harmonics to further reduce the current THD and to attain modulation indices up to square waveform. The superiority of the proposal in terms of current THD is substantiated through studies for multiple kinds of multiphase machines. The experiments are performed by using two six-phase induction motors with symmetrical/asymmetrical windings when 1 and 2 NPs are set.