Ditto the above replies, but additionally:
1) If you have a multi-section machine, be aware that stonewall in one section may drive one or more of the other sections into surge, which is potentially more damaging. If, for example, you have a 2-section compressor with a fixed outlet pressure, stonewall in section 2 may drive section 1 into surge due to the higher interstage pressure between the two sections. Similarly, stonewall or choke in section 1 could starve section 2 of core flow, thus driving the latter into surge if there is inadequate cold gas recycle to that section
2) Even if the compressor itself is not negatively impacted by operating in stonewall, be aware of potential negative impacts to the ancillary equipment and pipework. For example, downstream pipework velocities may be much higher than design, resulting in noise and possible vibration. A thermowell placed in the discharge line may see excessive vortex shedding, which could cause it to fail. So look at the bigger picture...
Best regards