You can also use the light overspill to work for the background and in the shot below.
If you are clever and can read the light, the split light can be used to illuminate the background. You can also use the light overspill to work for the background and in the shot below. This was one light (Red Head 1K) with barn doors. I used split lighting but positioned the model differently and allowed the light source to deviate and split into two. This allowed me to light the background and add exciting shadows from the barn doors on the light.