We combined Raman scattering and magnetic susceptibility to explore the properties of [(CH3)2NH2]Mn(HCOO)3 under compression. Analysis of the formate bending mode reveals a broad two-phase region surrounding the 4.2 GPa critical pressure that becomes increasingly sluggish below the order-disorder transition due to the extensive hydrogen-bonding network. Although the paraelectric and ferroelectric phases have different space groups at ambient-pressure conditions, they both drive toward P1 symmetry under compression. This is a direct consequence of how the order-disorder transition changes under pressure. We bring these findings together with prior magnetization work to create a pressure-temperature-magnetic field phase diagram, unveiling entanglement, competition, and a progression of symmetry-breaking effects that underlie functionality in this molecule-based multiferroic. That the high-pressure P1 phase is a subgroup of the ferroelectric Cc suggests the possibility of enhanced electric polarization as well as opportunity for strain control.