A research paradox currently lies in the design of miniaturized vibratory energy harvesters capable of harnessing energy efficiently from low-frequency excitations. To address this problem, this effort investigates the prospect of utilizing superharmonic resonances of a bi-stable system to harvest energy from excitation sources with low-frequency components. Towards that objective, the paper considers the electromechanical response of an axially-loaded clamped-clamped piezoelectric beam harvester with bi-stable potential characteristics. By numerically constructing the voltage-frequency bifurcation maps of the response near the super-harmonic resonance of order two, it is shown that, for certain base excitation levels, the harvester can exhibit responses that are favorable for energy harvesting. These include a unique branch of large-orbit periodic inter-well oscillations, coexisting branches of large-orbit solutions, and a bandwidth of frequencies where a unique chaotic attractor exists. In these regions, the harvester can produce power levels that are comparable to those obtained near the primary resonance.