Surface plasmon hybridization provides new perspectives for light manipulation at the nanoscale and related applications in nanophotonics. Multiple hybridization between metallic layers inside plasmonic nanocavities displays properties similar to atomic dressed states. In this Letter, we propose to numerically and analytically investigate the case of a multilayer structure composed of stacked metallic (M) and insulator (I) thin films. For a small number of MIM blocks, the system shows discrete hybridization schemes arising from plasmonic strong coupling. When the number of layers increases, multiple and stronger couplings occur and give birth to new modes which merge to form a plasmonic energy continuum. A schematic diagram of modes construction is presented to help the design of vertical nanocavities with specific properties such as plasmonic guiding.