In this article, we propose a model for multi-modes multi-electrodes piezoelectric energy harvester, and study its dynamics when associated with an electrical interface. We show that a multi-modes harvester allows to overcome the traditional power limit defined for single-mode harvesters, thanks to the effect of the second mode on the first one. We investigate this phenomenon with a resistive load, both theoretically and experimentally, for a piezoelectric energy harvester made with an inverted mass and four pairs of piezoelectric electrodes. Multi-modes resonances allow to fully exploit the potential of multi-modes energy harvesters, and open ways to design large bandwidth large power density energy harvesters.