Windows2000 is technically called NT5.0, while XP is called NT5.1. It is just a "dot one" incremental upgrade, the core code is the same. And upgrading to XP/Home (think "Lite" or "Castrati") would be a waste of money unless there was something very specific you needed in XP. There are a lot of nice tweaks in XP, but the core code is the same.
All three versions support 255 COM ports and no drivers or upgrades are needed, that support is right out of the box. HOWEVER, you'll of course need hardware to provide four COM ports and that may be more problematic. If you install an old "extra port" card you may have constraints on what IRQ values each port uses. NT can deal with that, but some older software which was written for DOS a Win3.x/9x will not work properly with anything besides COM1,2,3,4 (sometimes up to COM7). And then, that old software or hardware may "require" the COM port to be DOS-compatible using one of only two standard shared IRQ values, making it impossible to use all four at once.
If that's confusing...let's just say there is a lot of "it depends" when old hardware and software are involved. Not all of it will allow you to do what you want to do, on any computer.
If there are other devices in your computer that are already set up by the BIOS on any of the low COM port numbers (like an infrared IRDA port, or an internal modem) you may want to temporarily disable and uninstall them. Then install the new COM ports so they fall on COM1,2,3,4 and reinstall the other devices on the higher ports.
A lot will depend on the details of what you are trying to use, but the choice of Windows2000 /vs/ XP won't make any difference with this part of it, or how the COM ports can be installed.