Self-interacting dark matter (SIDM) is promising to solve or at least mitigate small-scale problems of cold collisionless dark matter. N-body simulations have proven to be a powerful tool to study SIDM within the astrophysical context. However, it turned out to be difficult to simulate dark matter models that typically scatter about a small angle, for example, light mediator models. We developed a novel numerical scheme for this regime of frequent self-interactions that allows for N-body simulations of systems like galaxy cluster mergers or even cosmological simulations. We have studied equal and unequal mass mergers of galaxies and galaxy clusters and found significant differences between the phenomenology of frequent self-interactions and the commonly studied large-angle scattering (rare self-interactions). For example, frequent self-interactions can produce larger offsets between galaxies and DM than rare self-interactions. Furthermore, the morphology of the galaxy distribution can differ significantly between frequent and rare self-interactions, especially in unequal-mass mergers. In general, we found late merger phases to be more interesting as differences between DM models have grown larger than shortly after the first pericentre passage.