Clusters of fullerenes (C60,C70)(n) are produced in a gas aggregation source and are multiply ionized in collisions with highly charged Xe(20+,30+) ions. Their stabilities and decay processes are analyzed with high-resolution time-of-flight mass spectrometry. Fullerene clusters in charge states up to q=5 have been observed and appearance sizes are found to be as small as n(app)=5, 10, 21, and 33 for q=2, 3, 4, and 5, respectively. The analysis of the multicoincident fragmentation spectra indicates a high charge mobility. This is in contrast to charge localization effects which have been reported for Ar(q+)(n) rare gas clusters. Clusters of fullerenes are found to be conducting when multiply charged.