Scatterplot 3D uses a scene box to render. This box understands the Scene3D messages in JSL. These messages implement most of OpenGL. You can define shapes and add them to a scene. Unfortunately, I do not see how to add shapes to an existing scatter plot. I tried to create a shape and add it, but it did not work, and there was no error message.
You might read the documentation about Three-Dimensional Scenes and try it on your own.
I do not understand what a 'plane' is in this case, and I might have misunderstood your request.