Host-parasite species pairs are known to coevolve, but how multiple parasites coevolve with their host is unclear. By using experimental coevolution of a host bacterium and its viral parasites, we revealed that diverse parasite communities accelerated host evolution and altered coevolutionary dynamics to enhance host resistance and decrease parasite infectivity. Increases in parasite diversity drove shifts in the mode of selection from fluctuating (Red Queen) dynamics to predominately directional (arms race) dynamics. Arms race dynamics were characterized by selective sweeps of generalist resistance mutations in the genes for the host bacterium’s cell surface lipopolysaccharide (a bacteriophage receptor), which caused faster molecular evolution within host populations and greater genetic divergence among populations. These results indicate that exposure to multiple parasites influences the rate and type of host-parasite coevolution.