Molecular solids that exhibit ferromagnetism are rare, and thus there is considerable interest in understanding the magnetic coupling mechanisms that operate in the few known examples(1). One such material is the charge-transfer salt NH4Ni(mnt)(2) . H2O, which consists of stacked planar metal ligands separated by ammonium cations. This salt is an insulator with localized spins that exhibit long-range ferromagnetic order at low temperatures (below 4.5 K)(2).3 Here we show that the Curie temperature demarcating the transition to the ferromagnetic state increases markedly with pressure until ferromagnetic order abruptly disappears at 6.8 kbar, indicating that the magnetic coupling is very sensitive to intermolecular separation. Using quantum-chemical calculations(3), we show that this pressure dependence arises from a competition between ferromagnetic coupling (resulting from nickel-sulphur intermolecular spin interactions), and antiferromagnetic coupling (from nickel-nickel interactions). We suggest that a similar interplay of spin-polarization effects might play a key role in determining the nature of the ground states (metallic, superconducting and so forth) observed in other molecular materials of this structural type(4,5).