Hi Matt,
Sorry for the delay in getting back to. The only way for this to be possible would be if you had a powerful video card (try running 4 videos at once and see if your computer can handle it).
The only way I can think of it happening would be if the software itself supported it - I'm not too familiar with webcams, but I'm sure someone has thought of this at sometime.
I just did a search in google -
split screen webcam - Google Search is what was returned.
Check them out, they may be what you're after.