Establishing the stability of cosmic fullerenes and fullerenic aggregates is extremely relevant for a variety of reasons. For instance, the emission features of C60 and C70 fall in the same spectral region as the Un-identified InfraRed (UIR) bands, which they could contribute to. To be able to contribute to the UIR emission, however, fullerenes must be able to survive long enough against the destruction mechanisms operating in the interstellar medium. In this study we focus on the effects of collisional processing, i.e., the bombardment by energetic ions and electrons. A recent experimental/theoretical study has shown that ion collisions with C60 clusters result in the dissociation of the cluster with the simultaneous formation of covalent fullerene dimers, which could play a role as DIBs carriers. We present here our first results about the collisional processing of C60 molecules and clusters by H, He and C ions in interstellar shocks. We have adapted the models that have previously been developed to successfully treat the collisional processing of PAHs in space. The nature of the interaction and the similarities between PAHs and fullerenes make this approach appropriate. In addition, our study shows that the formation of covalent dimers following ion collisions with C60 clusters is compatible with the astrophysical conditions under consideration.