We present a simple half-collision model that allows the approximate calcul
ation of absolute cross sections for multiple ionization by breaking this p
rocess down into a primary ionization event followed by a half-scattering e
vent in which additional electrons are ionized. As a critical test for the
feasability of this approach, we consider the double ionization of two-elec
tron systems, which we describe in terms of the single ionization of the "p
rimary" electron followed by impact ionization of the slow "secondary" elec
tron. For triple ionization of lithium, the model decomposes the three-elec
tron breakup process into a double ionization of the two inner electrons fo
llowed by electron-electron half-scattering of the receding electrons at th
e residual "spectator" 2s electron. We find surprisingly good agreement wit
h recent experimental data.