The coupling of photons to collective charge oscillations at the surface of a metal to form surface-plasmon polaritons enables strong confinement of electromagnetic near fields in the vicinity of photonic nanostructures. Even though surface plasmons are formed from bosons and fermions, this kind of near-field wave exhibits bosonic properties in the limit of many electrons. Here we show that the classical near-field dynamics of surface plasmons are defined by nonclassical processes of scattering among their constituent multiparticle subsystems. We isolate multiparticle plasmonic subsystems to demonstrate that their quantum dynamics are governed by either bosonic or fermionic processes of coherence. We also discuss the quantum-coherence properties of plasmonic fields excited by the vacuum fluctuations of the electromagnetic field. Our findings uncover multiparticle properties of electromagnetic near fields with important implications for quantum technology.