The landscape of high- and ultra-high-energy astrophysics has changed in the last decade, largely due to the inflow of data collected by large-scale cosmic-ray, gamma-ray, and neutrino observatories. At the dawn of the multimessenger era, the interpretation of these observations within a consistent framework is important to elucidate the open questions in this field. CRPropa 3.2 is a Monte Carlo code for simulating the propagation of high-energy particles in the Universe. This version represents a major leap forward, significantly expanding the simulation framework and opening up the possibility for many more astrophysical applications. This includes, among others: efficient simulation of high-energy particles in diffusion-dominated domains, self-consistent and fast modelling of electromagnetic cascades with an extended set of channels for photon production, and studies of cosmic-ray diffusion tensors based on updated coherent and turbulent magnetic-field models. Furthermore, several technical updates and improvements are introduced with the new version, such as: enhanced interpolation, targeted emission of sources, and a new propagation algorithm (Boris push). The detailed description of all novel features is accompanied by a discussion and a selected number of example applications.