I am not sure of the limitations of COM ports. I know for sure that it is no where near 4 though. typically, these are needed for external modems, terminal emulation and other devices but the need for a personal computer to have these is slowly diminishing. The COM ports are the the 9-pin connectors. You may only have 2 on your particular motherboard. Every computer doesn't have to have 4 installed. But, I've used devices developed by Digi
that house multi-communication port adapters. You install a card in one of your available PCI or ISA slots in your PC and then a cable connects to this card and has more available ports extending off of it. Sometimes they are called "octopus cables". They allow more COM port connections off of the cables. I've used these for serial interfacing with other computers. Typically, these COM ports off of the "octopus cable" would start with the last COM port on the machine. These ports would be labelled "P" and then a number. If there were 8 ports on the "octopus cable". Then they would be labelled "P1", "P2", "P3" and so on....
If you had 2 COM ports on the back of your computer (COM1 and COM2), then the port labelled "P1" would be COM3, "P2" would be COM4, "P3" would be COM5 and so on.....
I've personally seen and used a PC that had over 100 of these COM ports in hospitals.
Here is a picture of a "octopus cable"
Also, these can come in a range of sizes too. COM ports are just serial communication so they don't have to be the typical 9-pin fashion. They can be RJ-11 (Phone Line), RJ-45 (Ethernet), DB-25 (Looks like a Parallel port or LPT port....but it's serial), etc.