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We extended and generalized our previously developed semi-empirical method for the calculation of cross section functions (absolute value and energy dependence) for the single electron-impact ionization of the neutral and ionized fullerenes C 60q+ (q=0-3) to the calculation of multiple ionization processes of the neutral fullerenes C 60 and C 70 . Systematic trends and tendencies are highlighted and a detailed comparison with available experimental data is made. An attempt is also made to predict how the calculated cross sections scale with the size of the cluster/fullerene.