We have measured multiple-ionization yields of He , Ne , Ar , Kr , and Xe targets by 1.0 MeV/amu H2+ molecular ions for both the dissociative and nondissociative channels. Except for the case of the breakup of the H2+ into two protons, we have also determined the absolute cross sections for the multiple ionization of the targets. The ratios of multiple to single ionization for the nondissociative channel are similar to those for equivelocity protons, which, however, are consistently smaller than those for the breakup channels, for all charge states and targets. A simple analysis, based on the independent particle model, considering postcollisional time-delayed ionization for the Ne and Ar targets, evinces the importance of these mechanisms in the target multiple ionization and of the antiscreening in collisions where the projectile electron undergoes a transition.