An extended version of the statistical energy-deposition model is used for a description of multiple ionization of molecules by energetic ion impact. The energy transferred to the molecule during the collision is calculated as a function of the impact parameter within the local-electron-density approximation for a fixed molecular orientation. The fluctuating character of the deposited energy is taken into account by introducing a straggling of the energy transfer. For a given deposited energy the probability of multiple ionization of the molecule is assumed to be proportional to the volume of phase space available at the considered ionization state. The total ionization cross section is obtained by integrating over impact parameters and averaging over all orientations of the molecule. Sample calculations for collisions of He and F ions with N${}_{2}$ and CO molecules are presented and compared with experimental data. A dependence of the multiple ionization cross section on the molecular orientation is considered. A strong molecule alignment effect has been obtained in agreement with recent experimental findings.