Recent studies have demonstrated that the energetic vibrations of strategically designed negative stiffness inclusions may lead to large and adaptable damping in structural/material systems. Many researchers examine these features using models of bistable elements. From the viewpoint of system integration, bistable, negative stiffness elements often interface with positive stiffness elastic members. Under such conditions, the structural/material system may exhibit coexisting metastable states. In other words, the macroscopic displacement/strain remains fixed while the reaction force may vary due to internal change, similar to a phase transition. This coexistence of metastable states is not manifested in an individual (stand-alone) bistable element. Although the static and low frequency linear dynamics of structural/material systems possessing coexisting metastable states have been explored, much remains to be understood regarding the dynamics and energy dissipation characteristics of such systems when excited near resonance, where nonlinear dynamics are more easily activated and damping design is of greater importance. Thus, to effectively elucidate the enhanced versatility of damping properties afforded by exploiting negative stiffness inclusions in structural/material systems, this research investigates a mechanical module which leverages a coexistence of metastable states: an archetypal building block for system assembly. The studies employ analytical, numerical, and experimental findings to probe how near-resonant excitation can trigger multiple dynamic states, each resulting in distinct energy dissipation features. It is shown that, for lightly damped metastable mechanical modules, the effective energy dissipation may be varied across orders of magnitude via tailoring design and excitation parameters.