I sense some custom mainboard mounting systems, homemade backplanes, some creativity and a few hundred dollars could get you a very classy, wooden ( or steel, if you're VERY good ), home made 24u rack where you can put 6 4u machines in. Alternatively, if you're filthy rich, you could buy a 24 cabinet, complete with glass door and wheels. Very nice, very expensive, too.
Pretty shallow ( 18" ) 4u rackmount cases24 and 42u cabinets, if you're feeling rich today...