We report on the observation of multiple polariton modes, originating from an electronic coupling between quantum wells inside a planar microcavity. A series of excitonic transitions are measured for a bare quantum well stack and are precisely identified to electron-hole transitions originating from the coupling of the wells. When the quantum well stacks are placed at the antinode of a high Q-factor microcavity, a series of anticrossings is observed, which is characteristic of a multiplicity of polariton modes. This behavior is simulated using a coupled oscillator model accounting for the cavity mode and all allowed excitonic transitions.