It's mainly one of starting and stopping and the issue of hunting and surge if one compressor goes out of sync with the others. You also tend to need intercoolers between each one to avoid excessive heat and high temperature. What sort of pressure rise / service are you looking at? If you give a bit more of a back ground to your query, you will get more responses.
My motto: Learn something new every day
Also: There's usually a good reason why everyone does it that way