Natural stone would be much to heavy to attach with wire mesh/scratch coat method.
If you are referring to cultured stone,(man made lightweight stone) I would remove the Styrofoam and attach the mesh directly over tar paper/plywood.
P.S. A 1/2 in. depth scratch coat is difficult to accomplish over wire mesh. A new product (spiderlath)is available and more user friendly. Here is a YouTube video.