This can depend on the genre and desired results a little bit.  Separating the background vocals across the stereo mix is a good idea to achieve vibrant, full-sounding vocals. Think of how a choir might sound if you were standing in front of it. You would hear some of the singers on the right and some on the left. And you'd also hear some right in the middle.  When they start changing what they sing, it creates a texture. This is essentially what you're emulating when you're doing background vocals. Experiment separating full-sounding with separating the background vocals and see what you can come up with. There is a ton of room for creativity.