Triss is correct, it's the draw on the 12 volt line. Some newer power supplies have multiple taps, effectively separate outputs on the separate cables. Fans don't draw a lot of amps, so one more should be OK.
Personally, in addition to using fans to cool off my higher end PC's, I leave the left side door off. The end result is that the fans (especially the video card fan) run slower and the system is overall quieter with the left side door off and slower running fans. If you have a high end Intel CPU, it required that the inside of the case be not much hotter than room temperature (40 degrees Centrigrade), and I figured the easiest way to accomplish this was to open up the case. The other option is to use a case with a direct pipe to the CPU, but then there's still an issue with the video card, so I now use open cases.