Large transverse energy cross sections of 300 GeV/ c pions and protons on hydrogen have been measured with a segmented calorimeter covering the central rapidity region −0.88 < y < 0.67 and 2 π in azimuth. The selected events show large multiplicities and no jet-like event structure. Processes more complicated than the scattering of two constituents appear to dominate these inelastic collisions.