The sequential absorption of multiple infrared (IR) photons by isolated gas-phase species can lead to their dissociation and/or ionization. Using the newly constructed "Free-Electron Laser for IntraCavity Experiments" (FELICE) beam line at the FELIX facility, neutral C(60) molecules have been exposed to an extremely high number (approximately 10(23)) of photons/cm(2) for a total time duration of up to 5 micros. At wavelengths around 20 microm, resonant with allowed IR transitions of C(60), ionization and extensive fragmentation of the fullerenes are observed. The resulting photofragment distributions are attributed to absorption in fragmentation products formed once C(60) is excited to internal energies at which fragmentation or ionization takes place within the duration of the laser pulse. The high IR intensities available combined with the large interaction volume permit spatially resolved detection of the ions inside the laser beam, thereby disentangling the contributions from different IR intensities. The use of spatial imaging reveals intensity dependent mass distributions that are substantially narrower than what has been observed previously, indicating rather narrow energy distributions. A simple rate-equation modeling of the excitation process supports the experimental observations.