Can I run a stepper motor rated 12V with a 24V or above power supply?
The 12 V rating probably refers to the voltage you can apply to a coil indefinitely.  This limit is due to the heating it causes inside the motor.

You should be able to apply 24 for short periods of time without any problems.  It would be fine, for example, to drive the coils with 24 V controlled by PWM.  In that case, the PWM duty cycle should not exceed 50% on the long term.

Keep in mind that in steady state, the power dissipation goes with the square of the voltage.  Applying 24 V to the motor will cause 4x the heating it can handle.  It can be legitimate to do that for short periods of time, but then you have to ensure that the total average heating doesn't exceed what continuous 12 V would cause.  The time for this average can be a few seconds to a minute or more, depending on the size of the motor.

I once did a motor controller where the processor modeled the motor temperature internally.  When the motor was cold, it could be overdriven for short periods of time.  The controller kept track of the energy heating the motor, and assumed some decay to ambient.  It prevented driving the motor to the point of overheating.