When two hadrons collide, it is possible for several parton pairs to undergo (semi)hard interactions, more or less independently of each other. This phenomenon is called MultiParton Interactions, or MPIs for short. It is assumed to be essential for the structure of hadronic events, both minimum-bias events and underlying events. Typically high-multiplicity events are correlated with those that contain many MPIs.
An important aspect is that hadronic collisions can occur at varying impact parameters, and that central collisions should have a higher rate of MPIs than peripheral ones. Events that contain hard processes are likely to be biased towards central collisions, with more MPIs than average, thus larger underlying activity than in minimum-bias events. This phenomenon is sometimes called the pedestal effect.
MPIs can also occur in heavy-ion collisions, in fact even more so, and play an important part in the early stages of the collision history.