In the late 90's I had two sounds cards installed, think one was an AWE with the MIDI daughter card and the other was a SB16 or maybe a Vibra16 but I do know that I had to set IRQ's, addr's and IO ports differently on each card so there were no conflicts, then load drivers for both cards, each driver specifying the IRQ's, ports etc.
I cant remember what I did software wise, possibly set up what went where in the System Multimedia setup panel ?
I might have had to edit mmpm2.ini, so long ago, another world, a different life.
I ask this because today almost every new mainboard comes with two sound cards (or what it looks like two sound cards). One of the regular sound card (with ports in the front and other in the back) and other that is the HDMI sound out port.
Just went back and reread your post

The above bit is 'normally' simply mixing, not two different sound cards. ie, you select were you want the outputs to go to depending on program or inputs.
I guess it comes down to the motherboard though, a manufacturer might have made an upmarket MB for a vertical market maybe.
Some audio chipsets have completely separate input paths and completely separate output paths but its all done with high speed digital multiplexing and pathways before it hits the DAC's, so you can do some fancy stuff but it all comes down to the actual mixing. I have seen some where a sound card with 4 completely separate dual channels(read chipsets) on it, that I would classify as 4 sounds cards but it uses the one driver (not OS/2 unfortunately). Other stuff, its simply easier to use an external USB connected mixer.
[edited again, my speeling is bad when I get tired]