The idea of a supersonic biplane is quite old, certainly back to von Karman, and not necessarily silly.
I've seen a picture of a von Karman design where the lower wing sweeps back and the upper wing sweeps forward and the tips angle to join which also gave improved structural strength (rather important on forward swept wings). I can't find a link to a picture unfortunately. At the time we were wondering about using the shock wave interaction to get a reduced acoustic signature for an SSBJ design. The original von Karman intent was to improve L/D. The best link I can find is :
1958 | 1- - 0474 | Flight Archive
Regards,