We demonstrate a double Rabi splitting totaling 348 meV in an Ag nanocavity embedding of methylene blue (MB) dye layer, which is ascribed to the equilibrium state of monomer and dimer coexistence in MB dye. At low dye concentration, the single-mode strong coupling between the monomer exciton in MB dye and the Ag nanocavity is observed. As the dye concentration is increased, three hybridized plexciton states are observed, indicating a double Rabi splitting (178 and 170 meV). Furthermore, the double anti-crossing behavior of the three hybrid states is observed by tuning the Ag nanocube size, which validates the multi-mode strong coupling regime. It shows clear evidence on the diverse exciton forms of dye molecules, both of which can interact with plasmonic nanocavity, effectively. Therefore, it provides a good candidate for realizing the multi-mode strong coupling.