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We study steady state phases of a one-dimensional array of Rydberg atoms coupled by a microwave (MW) field where the higher energy Rydberg state decays to the lower energy one via single-body and collective (superradiant) decay. Using mean-field approaches, we examine the interplay among the MW coupling, intra-state van der Waals (vdW) interaction, and single-body and collective dissipation between Rydberg states. A linear stability analysis reveals that a series of phases, including uniform, antiferromagnetic, oscillatory, and bistable and multistable phases can be obtained. Without the vdW interaction, only uniform phases are found. In the presence of the vdW interaction, multistable solutions are enhanced when increasing the strength of the superradiant decay rate. Our numerical simulations show that the bistable and multistable phases are stabilized by superradiance in a long chain. The critical point between the uniform and multistable phases and its scaling with the atom number is obtained. Through numerically solving the master equation of a finite chain, we show that the mean-field multistable phase could be characterized by expectation values of Rydberg populations and two-body correlations between Rydberg atoms in different sites.