It applies to both. In SP you are essentially the server and the client. Any calculations the server would normally do is being done by your client. In all the test you ran you where the server and the client (same system running both). For true MP testing you need to have the host (server) running on a different physical machine.
Try occlusion testing. Create a large ceiling out of a single cube mesh and place it under the large platform. Your stuttering only happens at specific points under the platform which I assume is a single mesh. You could also create a wall with an opening to pass through out of two cube meshes to occlude distant objects/components.