Convergence to low-energy responses arising from coexistence of multiple stable nodes is the main drawback of a nonlinear energy harvester preventing it from efficient wideband operation. A switching circuit with a boost-like topology has been proposed in this paper to overcome this substantial challenge. The circuit uses the energy harvested by the device to trigger it to jump from the low- to high-energy response. The performance of the proposed harvesting system when subjected to single harmonic excitations covering a wide range of frequencies is verified through both analytical and numerical investigations. Results indicate that by proper selection of timing parameters of the circuit including ON-time period of the switches together with the phase differences between the switching signals and the mechanical excitation, the applied electrical perturbation will be able to trigger the nonlinear resonating beam to jump from a low-energy response to the basin of attraction of the high-energy one within the whole frequency band in which a multivalued solution exists. Also, a probabilistic study is performed on a system with random phases of switching signals which shows that a successful switching from low- to high-energy response is achievable with a probability more than 80% by just controlling the ON-time period of the switch within the proper ranges with respect to the excitation frequency.