I client recently asked if they could plug a surge protector to their UPS (Uninterruptible Power Supply) since they did not have enough UPS outlets for their equipment.
Without getting into technical details, exceptions and considerations, the short answer is NO. However, depending on the load and UPS size you can plug in a power strip to yield additional outlets. Just make sure you are using a power strip without surge protection, it is the surge protection that will cause the problems.
By the same token you should also never plug a UPS into a surge protector.