The interaction of coexisting structural instabilities in multiferroic materials gives rise to intriguing coupling phenomena and extraordinarily rich phase diagrams, both in bulk materials and strained thin films. Here we investigate the multiferroic BiMnO3 with its peculiar 6s2 electrons and four interacting mechanisms: electric polarity, octahedra tilts, magnetism, and cooperative Jahn-Teller distortion. We have probed structural transitions under high pressure by synchrotron x-ray diffraction and Raman spectroscopy up to 60 GPa. We show that BiMnO3 displays under pressure a rich sequence of five phases with a great variety of structures and properties, including a metallic phase above 53 GPa and, between 37 and 53 GPa, a strongly elongated monoclinic phase that allows ferroelectricity, which contradicts the traditional expectation that ferroelectricity vanishes under pressure. Between 7 and 37 GPa, the Pnma structure remains remarkably stable but shows a reduction of the Jahn-Teller distortion in a way that differs from the behavior observed in the archetypal orthorhombic Jahn-Teller distorted perovskite LaMnO3.