  We investigate several ingredients for a theory of multiple hard scattering
in hadron-hadron collisions. Issues discussed include the space-time structure
of multiple interactions, their power behavior, spin and color correlations,
interference terms, scale evolution and Sudakov logarithms. We discuss
possibilities to constrain multiparton distributions by lattice calculations
and by connecting them with generalized parton distributions. We show that the
behavior of two-parton distributions at small interparton distances leads to
problems with ultraviolet divergences and with double counting, which requires
modification of the presently available theoretical framework.
