You *could* run two computers if you wanted to. I think that would be inconvenient. You would only need one JRiver license though; MC lets you install on several of your own computers as part of it's normal licensing. Which is really nice!
You can definitely set up two or more DACs on one computer and have MC use them independently. As Jim said, you can set up a Zone for each DAC. Zones are playback targets. You have a separate playing now area for each zone. So you could run them at the same time if you wanted to. Or just stop and start playback in each zone as you like.
I do this with a speaker system and headphones. Each have their own DAC. When I want to hear speakers, I put songs in the speaker zone. When I want to listen to headphones, I play songs in the headphone zone. I even copy playing now from one to the other when I want to switch.
Zones are pretty easy to set up and use. There are a few details here:
http://wiki.jriver.com/index.php/ZonesBrian.