Where you can have a problem is getting com1 and com3 to work together or com2 and com4 to work together. com1 and com3 share an interrupt as does com2 and com4. You can assign two COM ports with the same interrupt as long as you don't use the two ports at the same time. For example, com1 to serial port used by a digital camera and com3 to a serial port used by a scanner. As long as the applications are run separately and do not attempt to access the ports simulataneously, they will both work. Try to download images from your camera and use your scanner at the same time, NO. Then you run into a resource clash.
I have seen four ports in use simultaneously using only 2 IRQ's. You will probably have to set