Modelling multiple partonic interactions in hadronic events is vital for understanding minimum-bias physics, as well as the underlying event of hard processes. A brief overview of the current Pythia 8 multiple interactions (MI) model is given, before looking at two additional effects which can be included in the MI framework. With rescattering, a previously scattered parton is allowed to take part in another subsequent scattering, while with enhanced screening, the effects of varying initial-state fluctuations are modelled.
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