Running it above base frequency but keeping the V/f ratio at nominal rating.
Expanded version:
Dont think of this as a way to increase the HP, that's irrelevant. HP is just a shorthand notation expressing torque at a given speed. What we really use most of the time is the torque, then deal with the speed that the motor runs at to give us that.
When running a motor from a VFD, the VFD allows the motor to produce full rated torque at any speed by maintaining the ratio of voltage and frequency, the V/Hz ratio, at what the motor was deigned for. But a VFD cannot create voltage that was not there on the input side, so when you reach the maximum line voltage, but want to increase the speed beyond the line frequency speed, you begin to lower that V/Hz ratio, which results in a loss of torque. For example if I want to run a 60Hz designed motor at frequencies from 10 to 120Hz, once I get over 60Hz, torque drops off and because losses increase, the net torque drops even faster than that change in speed and in some cases can eventaully result in the motor not producing even enough torque to spin its own rotor.
So the supercharge trick is to lower the motor's V/Hz ratio up front by connecting it as a lower voltage motor like 230V, program the VFD to reach 230V at 60Hz, then because the line voltage is 480, I can continue to increase the frequency to 120Hz and still get my full torque from the motor. The fact that the HP technically increases is coincidental, but not germane.
Cons: (major ones)
MOST motors are not designed to do this; there are limits due to the speed rating off the bearings, the cooling of the motor because cooling fan efficiency can drop faster than the increase in heat, and mechanical balance issues can make the motor, or whatever is connected to it, vibrate to destruction. All of those issues and more must be considered and thoroughly investigated.