  Recent experimental data have established some of the basic features of
multiple interactions in hadron-hadron collisions. The emphasis is therefore
now shifting, to one of exploring more detailed aspects. Starting from a brief
review of the current situation, a next-generation model is developed, wherein
a detailed account is given of correlated flavour, colour, longitudinal and
transverse momentum distributions, encompassing both the partons initiating
perturbative interactions and the partons left in the beam remnants. Some of
the main features are illustrated for the Tevatron and the LHC.
