Nanostructured plasmonic metal systems are known to enhance greatly variety of radiative and nonradiative optical processes, both linear and nonlinear, which are due to the interaction of an electron in a molecule or semiconductor with the enhanced local optical field of the surface plasmons. Principally different are numerous many-body phenomena that are due to the Coulomb interaction between charged particles: carriers (electrons and holes) and ions. These include carrier-carrier or carrier-ion scattering, energy and momentum transfer (including the drag effect), thermal equilibration, exciton formation, impact ionization, Auger effects, etc. It is not widely recognized that these and other many-body effects can also be modified and enhanced by the surface-plasmon local fields. A special but extremely important class of such many-body phenomena is constituted by chemical reactions at metal surfaces, including catalytic reactions. Here, we propose a general and powerful theory of the plasmonic enhancement of the many-body phenomena resulting in a closed expression for the surface plasmon-dressed Coulomb interaction. We illustrate this theory by computing this dressed interaction explicitly for an important example of metal-dielectric nanoshells, which exhibits a reach resonant behavior in both the magnitude and phase. This interaction is used to describe the nanoplasmonic-enhanced Foerster energy transfer between nanocrystal quantum dots in the proximity of a plasmonic nanoshell. Catalysis at nanostructured metal surfaces, nonlocal carrier scattering and surface-enhanced Raman scattering are discussed among other effects and applications where the nanoplasmonic renormalization of the Coulomb interaction may be of principal importance.