The reaction He3(+,pp)p was measured at T=350 and 500 MeV in a kinematically complete experiment. Separate contributions from two-body and three-body pion absorption are clearly seen in recoil momentum distributions. The two-body angular distributions closely follow the shape of the free dpp cross section, although the number of deuterons estimated from the two-body yield is larger than the value 1.5 expected from isospin coupling and observed previously at lower energies. Comparison with a simple impulse approximation model suggests some of the enhancement may arise from binding of the quasideuteron, although absorption on T=1 (pn) pairs and the higher density of He3 may also be a factor. The strength of the three-body component falls off with bombarding energy with roughly the same slope as for the two-body component, and accounts for 45% of the total absorption cross section, a larger fraction than reported previously below the (3,3) resonance. The three-body matrix element M32 displays an angular dependence at both energies which is suggestive of initial-state interactions. No evidence of final-state interactions is seen.