One practical problem, if it's saturated steam, is that by increasing pressure, you're increasing the condensation point, so a lot of the steam will keep turning to liquid water without any considerable pressure growth. If you take 10l of dry air at 1 bar and compress it to 2 bar, you get about 5l of the compressed air. But if you take saturated steam - you'll get a glass of water at a little more than 100C and probably less than a liter of steam of 2 bar.
There will be a lot of other minor problems, like a compressor that operates at 100+C in high moisture, safety and so on, but it all boils down to: WHY?
It's very easy to increase pressure of steam by superheating it. This is the primary method how all turbines are propelled. Sometimes superheated steam will even be used to propel turbocompressors of other materials, it's so easy and ubiquitous. What purpose would compressing the saturated steam with a compressor serve? You won't even get the work back, you'll just get a lot of hot, compressed liquid water (that can be obtained by much easier means).