The present contribution is a follow-up of a recently conducted study to derive a data-driven model for the breakage of agglomerates by wall impacts. This time the collision-induced breakage of agglomerates and concurrently occurring particle agglomeration processes are considered in order to derive a model for Euler--Lagrange methods, in which agglomerates are represented by effective spheres. Although the physical problem is more challenging due to an increased number of influencing parameters, the strategy followed is very similar. In a first step extensive discrete element simulations are carried out to study a variety of binary inter-agglomerate collision scenarios. That includes different collision angles, collision velocities, agglomerate sizes and powders. The resulting extensive database accounts for back-bouncing, agglomeration and breakage events. Subsequently, the collision database is used for training artificial neural networks to predict the post-collision number of arising entities, their size distributions and their velocities. Finally, it is shown how the arising data-driven model can be incorporated into the Euler--Lagrange framework to be used in future studies for efficient computations of flows with high mass loadings.