Speed of Synchronous Motor

Disconnect it from a power source and connect another spinning device to it that is turning at greater than 1500RPM.

Or do the same without disconnecting it, and overload it for a short time before it over heats, catches fire, melts the bearings and the stator crashes into the rotor.

A sufficient overrunning load could cause pole-jumping in the faster direction.

or you can still disconnect one pair of poles, and stay with "almost" a synchronous engine

Highly inadvisable.

yes, but no safety issues were asked! if the connections were nicely made it would old for some time

supply it with more than 50Hz or point it downhill??

In theory, if you apply 60 Hz supply, the 50 Hz motor will run at 1800 rev/min. In practice, it will run but you would need to be sure the rotor/bearings are mechanically OK at 20% over-speed. You would also have to accept a reduced torque capability compared to 50Hz, due to having 50/60 of the magnetizing current at 60 Hz, 230V, also increased cooling fan losses at the higher speed. Some motors are used with electronic variable frequency drives, which enable a wide speed range - even allowing "voltage proportional to frequency" to maintain the torque capacity over the speed range.

The plant I used to work on had a 300Hz genny, how fast do you want the motor to run?

Did you heard of Rotating Magnetic Field(RMF)?

The answer 67model has suggested is the best one

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