Running it like two tandems side by side is an idea. Although the solid rear axle could hinder cornering, I'd like to keep it solid due to maintain some sort of traction. I've seen one home made Quadracycle, but it appeared to have the left/right wheels completely independent. I'm not quite sure yet how to make them spin at different speeds during cornering, which would require some sort of differential.
I've looked for a few hours for Quadracycles, but whatever I did find didn't really shed any light on the design.