=Mn,Co,Ni)

We combine magnetization and infrared spectroscopy to unveil the B-T phase diagrams and vibrational properties of the [(CH₃)₂NH₂]M(HCOO)₃ (M=Mn,Co,Ni) family of multiferroics. While the magnetically-driven transition to B_C in the Mn analog takes place at 15.3 T, much higher fields are required to saturate the Ni and Co materials. Analysis of the infrared spectrum of the Mn and Ni compounds across T_C reveals splitting of the formate bending mode which functions as an order parameter of the ferroelectric transition. By contrast, the Co complex reveals a surprising framework rigidity where the ferroelectric state is driven solely by counterion freezing. With magnetic field, the Mn (and most likely, the Ni) materials engage the formate bending mode to facilitate the transition to the fully saturated magnetic states, whereas the Co complex adopts an alternate mechanism involving formate stretching distortions. Similar structure-property relations involving substitution of transition metal centers and control of the flexible molecular architecture are likely to exist in other molecule-based multiferroics.