We have determined absolute charge transfer and fragmentation cross sections in He2++C60 collisions in the impact-energy range 0.1-250 keV by using a combined experimental and theoretical approach. We have found that the cross sections for the formation of He+ and He0 are comparable in magnitude, which cannot be explained by the sole contribution of pure single and double electron capture but also by contribution of transfer-ionization processes that are important even at low impact energies. The results show that multifragmentation is important only at impact energies larger than 40 keV; at lower energies, sequential C2 evaporation is the dominant process.