Vibration energy harvesting using the piezoelectric effect has recently attracted significant attention from scholars. The main concern in the research of piezoelectric vibration energy harvesters is to improve the operating bandwidth and output power in low-frequency vibration environments with random and time-varying nature. A novel piezoelectric vibration energy harvester (PVEH) with three parallel cantilevers and repulsive magnet pair structures is proposed in this work to achieve the above goal. The proposed PVEH has the potential to take full advantage of the synergistic effect of the multi-frequency and magnetic nonlinear performance enhancement techniques. The characteristics of the harvester are systematically studied by theoretical modeling, simulation, and experiments. The influence of the critical parameters (i.e. the tip mass of the inner beam, the tip mass of the outer beam, and the magnet spacing) on the output performance of the PVEH is discussed and optimized in detail, and then the internal mechanism of the proposed energy harvesting method based on multi-frequency and magnetic cooperation is revealed. The results show that the improvement rate of the output power of the fabricated prototype under the condition of first-order and second-order operating frequency reaches 23.35% and 38.10%, respectively, compared with the non-magnetic structure. Finally, the optimal configuration of the harvester (Mi=6.70 g, Mo=5.00 g, s=22 mm) obtains a maximum half-power bandwidth of 1.052 Hz and a maximum output power of 2.80 mW under 0.2g with 0.155 MΩ load resistance. The proposed energy harvesting system is expected to be a promising alternative to efficient vibration energy harvesters.