A general theoretical procedure is developed that treats the fragmentation of a polyatomic cluster ion following excitation by a fast rare gas atom. The process involves multiple electronic states of the cluster ion that are described by the diatomics-in-molecule (DIM) procedure. The interaction of the cluster ion with the rare gas atom is obtained by extending the DIM model and by including three-center interactions. The atom-cluster collision is treated using the semiclassical path procedure and the sudden approximation for the cluster. Finally, the fragmentation is studied using the trajectory surface hopping procedure. The method is applied to the Na-3(+)-He system, which can fragment into three product channels. For each channel doubly differential cross sections are computed and compared with the available experimental data. The calculations give much insight into the fragmentation process of Na-3(+). (C) 2000 American Institute of Physics. [S0021-9606(00)00916-8].