This study presents a theoretical framework for the propagation of a compound consisting of N interacting particles in a multicenter potential. A novel Green operator approach is proposed that disentangles the geometrical and dynamical properties of the scatterers from the internal evolution of the projectile compound. Furthermore, the transition operator for the scattering from the multicenter potential is expanded in terms of many-body scattering path operators, which in turn are expressed in terms of single site transition operators that are amenable to computations. To deduce the correlated many-body Green operator of the scattering compound, a cumulative method is designed that reduces the problem to the evaluation of Green operators of systems with a reduced number of interacting particles. This is particularly useful for efficient calculations and encompasses the usual perturbative approaches.