Two key challenges in diffusion-based molecular communication are low data rates and accounting for the geometry of the fluid medium in the form of obstacles and the boundary. To reduce the need for the receiver to have knowledge of the geometry of the medium, binary equilibrium signaling has recently been proposed for molecular communication with a passive receiver in bounded channels. In this approach, reversible chemical reactions are introduced at the transmitter and the receiver in order for the system to converge to a known equilibrium state. This provides a means of designing simple detection rules that only depend on the transmitted signal and the volume of the bounded fluid medium. In this paper, we introduce multi-level equilibrium signaling, which allows for higher data rates via higher order modulation. We show that for a wide range of conditions, with appropriate receiver optimization, multi-level equilibrium signaling can outperform conventional concentration shift keying schemes. As such, our approach provides a basis to improve data rates in molecular communications without the need to increase the complexity of the system by exploiting techniques such as multiple information-carrying molecules.