Since the motor field rotation speed is determined by frequency only, running a motor above its base speed will cause the rotor to try to spin up to the higher speed. Clearly, it will need to have adequate torque to get to the higher speed.
That indicates that we need to focus on the motor torque curve over the motor base speed and compare it to the load torque curve at these same speeds. If, at any point, the motor matches or falls below load speed, further acceleration is impossible and the speed will not increase beyond that point.
It is true that virtually all motors operate with a constant torque characteristic from zero to nameplate base speed but, above nameplate speed, the torque will be reduced by the inverse of the overspeed ratio. So, for example, if you are up to 70 Hz on a 60 Hz motor, the speed will be 70/60 times nameplate but the torque will be 60/70 times normal rated torque. This behavior continues up to a point where the motor internals no longer can deal with the higher frequencies. At that point, the torque starts to fall off even faster and stalling follows soon after. Each motor design is different in this respect--some inverter duty four pole motors are guaranteed to keep torque in this proportion (constant hp) up to double base speed while many others, especially slow speed motors and early designs, will not hold this proportional relationship up to even 80hz on a 60hz motor.
A further complication is that, while continuous rated motor torque follows the above inverse ratio rule, the short term overload torque available from the motor comes down as the SQUARE of the overspeed ratio. So, at double base speed on most motors, there is no overload capacity left at all.
As to mechanical issues, any NEMA or IEC motor with a cast aluminum rotor excluding two pole designs can be taken to at least 90 Hz without any real balance or bearing concerns. On two pole motors, I quit at 4500rpm mainly for cooling fan concerns.
The bottom line is that using the motor overspeed capabilities is good design practice as long as the limitations are taken into account. For myself, under 100hp and excluding two pole motors and increasing torque loads, I try to design the power train so full speed on the load is 90Hz on the motor. Lots of good things happen when you follow that rule.
Hope this helps answer your questions.