I've provided as many as six feeds on one computer.
Now I typically run fewer feeds on each of seven computers.
Below is a desktop screen capture of one of my oldest XP computers.
It's providing 3 feeds using ScannerCast, logging 4 feeds with ScanRec Pro, and listening to 7 feeds with WINAMP.
I have at least two sound cards in all of my computers. Four in most of them.
One thing you don't want to try is run multiple, identical sound cards. You can wind up with conflicts and/or lots of confusion.
This particular computer is providing two feeds using sound cards and one using a USB sound device.
C-Media, NVIDIA, and a generic SSS USB Headphone Set that I bought a dozen of a few years ago.
By the way, if you're wondering how I keep it all straight ....... I have a cheat sheet of all my feeds and computers in MS Word format.