The cross section for inclusive multipion production in the pp-->ppX reaction was measured at COSY-ANKE at four beam energies, 0.8, 1.1, 1.4, and 2.0 GeV, for low excitation energy in the final pp system, such that the diproton quasiparticle is in the 1S0 state. At the three higher energies, the missing-mass M_{X} spectra show a strong enhancement at low M_{X}, corresponding to an Abashian-Booth-Crowe effect that moves steadily to larger values as the energy is increased. Despite the missing-mass structure looking very different at 0.8 GeV, the variation with M_{X} and beam energy are consistent with two-pion production being mediated through the excitation of two Delta(1232) isobars, coupled to S and D states of the initial pp system. There is no sign of any resonancelike structure in the energy dependence of the type recently observed for the pn-->dpi;{0}pi;{0} total cross section.