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Multiphase machines have significant benefits over their three-phase counterparts. One of them is the possibility of further exploiting the dc-link voltage by injecting non-torque-related voltage harmonics in the $xy$ planes. This allows reaching higher modulation indices in the overmodulation (OVM) region of pulsewidth modulation (PWM) while avoiding torque ripple in motors with negligible space harmonic effects. The most prominent OVM techniques are those based on the instantaneous minimization of the $xy$ voltage. These methods were devised just for five-phase drives and have the drawback that they lack generality. This article overcomes this limitation by proposing an OVM strategy for symmetrical induction motor drives with any odd phase number $n$. The proposal achieves the minimum voltage distortion, and consequently, it greatly mitigates the $xy$ current distortion. Indeed, it attains the lowest current distortion compared with the existing techniques. It relies on carrier-based PWM in its design and implementation stages, and accordingly, it is much simpler than previous methods. Furthermore, the inverter switching frequency (loss) is substantially reduced. Theoretical assessments are given for drives with odd $n$ between 5 and 11. The experiments are performed with a symmetrical nine-phase induction motor with a single neutral point.