We study the out-of-equilibrium dynamics of dissipative gases of atoms excited to two or more high-lying Rydberg states. This situation bears interesting similarities to classical binary (in general p-ary) mixtures of particles. The effective forces between the components are determined by the inter-level and intra-level interactions of Rydberg atoms. These systems permit to explore new parameter regimes which are physically inaccessible in a classical setting, for example one in which the

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... res exhibit non-additive interactions. In this situation the out-of-equilibrium evolution is characterized by the formation of metastable domains that reach partial equilibration long before the attainment of stationarity. In experimental settings with mesoscopic sizes, this collective behavior may in fact take the appearance of dynamic symmetry breaking.