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Owing to their overall low energy scales, flexible molecular architectures, and ease of chemical substitution, molecule-based multiferroics are extraordinarily responsive to external stimuli and exhibit remarkably rich phase diagrams. Even so, the stability and microscopic properties of various magnetic states in close proximity to quantum critical points are highly under-explored in these materials. Inspired by these opportunities, we combined pulsed-field magnetization, first-principles calculations, and numerical simulations to reveal the magnetic field–temperature (B–T) phase diagram of multiferroic (NH₄)₂FeCl₅⋅H₂O. In this system, a network of intermolecular hydrogen and halogen bonds creates a competing set of exchange interactions that generates additional structure in the phase diagram—both in the vicinity of the spin flop and near the 30 T transition to the fully saturated state. Consequently, the phase diagrams of (NH₄)₂FeCl₅⋅H₂O and its deuterated analog are much more complex than those of other molecule-based multiferroics. The entire series of coupled electric and magnetic transitions can be accessed with a powered magnet, opening the door to exploration and control of properties in this and related materials.