The objective of this paper is twofold: first to illustrate that nonlinear modal interactions, namely, a two-to-one internal resonance energy pump, can be exploited to improve the steady-state bandwidth of vibratory energy harvesters; and, second, to investigate the influence of key system’s parameters on the steady-state bandwidth in the presence of the internal resonance. To achieve this objective, an L-shaped piezoelectric cantilevered harvester augmented with frequency tuning magnets is considered. The distance between the magnets is adjusted such that the second modal frequency of the structure is nearly twice its first modal frequency. This facilitates a nonlinear energy exchange between these two commensurate modes resulting in large-amplitude responses over a wider range of frequencies. The harvester is then subjected to a harmonic excitation with a frequency close to the first modal frequency, and the voltage–frequency response curves are generated. Results clearly illustrate an improved bandwidth and output voltage over a case which does not involve an internal resonance. A nonlinear model of the harvester is developed and validated against experimental findings. An approximate analytical solution of the model is obtained using perturbation methods and utilized to draw several conclusions regarding the influence of key design parameters on the harvester’s bandwidth.