The first and by far the most important question when determining the maximum speed is "what is the maximum SAFE speed?".
If you are sure you are below that, then the issues are all about the motor, not the drive.
First, are you sure the available continuous motor torque is higher than the required continuous load torque?
Second, are you sure the available short-term overload torque is higher than the required short-term overload torque? Remember, the short-term torque goes down as a function of the inverse of overspeed SQUARED.
Can the power train take the extra speed? Some gearboxes cannot due to lubricant foaming issues.
While iron losses may increase, the increase will be very small and insignificant. The higher fan speed will handle any increase in heat easily.
Finally, make sure the motor is mechanically capable of the higher speed. In a 5hp 4 pole motor, there are few concerns. In a 300hp 449TS frame two pole motor, there are major concerns, some even involving life safety.