In common rotary piezoelectric (PZT) frequency up-converting energy harvesters, impact or nonimpact frequency up-conversion technologies are used. For low separation distances between the magnets in nonimpact cases, when weak excitation is applied, depending on some parameters such as separation distance between the magnets, eccentric proof mass may be unable to overcome the magnetic potential between the magnets, and thus, the extracted power of the harvester lowers. To increase the harvester power output, the use of an additional pair of magnets, called the assisting part, is proposed in this paper. For different harmonic excitations, the generated powers of the harvester with and without assisting part have been compared to each other. It is found that by appropriately adjusting the separation distance, the use of such part can increase the generated power in most cases. Using a real-world multifrequency multi-amplitude excitation, the ability of the proposed idea to increase the extracted power is investigated. It is found that the maximum generated power of the device can effectively increase to more than two times. In order to check the accuracy of the applied mathematical modeling, some experiments have been conducted.