It seems like diffusion is most likely what you're looking for. Diffusion will not only soften the light that hits the subject, but significantly lessen the shadows that the subject casts. Lots of things can be used for diffusion, bedsheets, table cloths, silk from the fabric store, shower curtain. But two things are really important with diffusion material. You need make sure they are color neutral, picks any tint they have will transfer into the light. Or you at least need to be aware of any color shift they are causing so you can correct for it. The other thing is to know that any material that is the right amount of translucent to soften the light effectively, while still letting it through, will take about 1-2 stop of light out of your situation. So, if the lights you are using are already bordering on not bright enough, diffusion will only make it worse.
Softness of light is one of two main thing that will help. The other is getting your subject further from the wall. Due to the light fall off properties related to the inverse square law, the light-to-subject/light-to-background ratio will have a huge effect on how the background shadows. To more space between you have between your subject and your background, the more you end up with two independent planes of lighting. Then if you add in more light that is specific for the background, you have complete control over how you want the light on each to look.
DOing the thrre point lighting or just adding in fill, is generally a good idea, but I feel like in this situation with hard light sources and close quarters, that it would really actually just result in have more shadows on the floor and other walls. With hard light, it's really hard for fill light to take care of the shadow. With a soft light source, the shadow won't have a hard edge like it will from a hard source. Since the shadows is more of a graduated transition, it doesn't take much fill light to significantly lessen the shadow. But with hard light, it's a razor cut line from shadows to not shadow. So that line will always be there. You can add fill to make the contrast ratio less, but the transition line will always be present.
Your best bet is definitely to try and soften the light source.
The other thing is that, depending on what the scene is, you can just leave it like that. If your scene is supposed to be a dark basement, that its what they look like. It's usually a single, hard, high angle light source, that has deep shadows and hard transitions. Nothing wrong with that if that is what the scene is.
Keep experimenting, and good luck!
Cheers,
Ben
