A recently proposed classical-trajectory dynamical screening model for the description of multiple ionization and capture during ion-water molecule collisions is extended to incorporate dynamical screening on both the multi-center target potential and the projectile ion. Comparison with available experimental data for He$^{2+}$ + H$_2$O collisions at intermediate energies (10-150 keV/u) and Li$^{3+}$ + H$_2$O at higher energies (100-850 keV/u) demonstrates the importance of both screening mechanisms. The question of how to deal with the repartitioning of the capture flux into allowed capture channels is addressed. The model also provides insights for data on highly-charged projectile ions (C$^{6+}$, O$^{8+}$, Si$^{13+}$) in the MeV/u range where the question of saturation effects in net ionization was raised in the literature.
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