How can I add privacy to my stone fence without having to build on to it?

Without an actual site visit, it's difficult to know what might work best in your situation. You may be able to add a light weight topper to your stone fence--something like a lattice panel. Or perhaps attaching a lattice panel to the front of the wall, extending above it. If in-ground planting isn't an option, you could grow vines in container gardens placed next to the wall.