When a double barrier semiconductor structure is biased near a tunneling resonance, charge can accumulate in the central quantum well. We report photoluminescence measurements of the 2D charge density over the full range of a tunneling resonance with emphasis on the region of multistability. An active load line technique was used to bias the device into this region, which is otherwise inaccessible. The charge density versus current graph shows hysteresis and the plasmon excitation, which is a strong feature in the current-voltage characteristic, appears only weakly. Both these results are consistent with a model calculation based on charge conservation and the electron-electron interaction.