Well as already pointed out, it is not practical.
BUT there has been research into supersonic biplane configurations, because it is possible to take advantage of compressible flow in such a configuration to produce a very low-drag lifting device. I'm afraid my uni days are too long ago to remember the exact details, but basically the idea was to arrange the separation of the biplanes so that at a given mach number the reflected internal shock waves cancelled out the external shock waves.