This project aims at a better description of processes involving multiple vector bosons at the LHC, in particular vector-boson scattering and multi-boson s-channel production. It will include next-to-leading order QCD and electroweak corrections, as well as the modelling of realistic final states with an efficient Monte Carlo event generator. The project also involves the implementation of higher-dimensional operators in an effective field theory framework, and subsequent phenomenological studies of the sensitivity of such processes to BSM effects. To achieve this goal, substantial technical advances need to be made, both on the loop amplitude representation as well as on the phase space sampling side. Modern machine learning methods will be explored to push the efficiency of such a Monte Carlo framework to a higher level.