The complexes [(Mn3O)-O-III(Et-sao)(3)(O2CPh(Cl)(2))(MeOH)(3)(H2O)] (1), [(Mn3O)-O-III(Et-sao)(3)(ClO4)(MeOH)(3)] (2), [(Mn3O)-O-III(Et-sao)(3)(O2Ph(CF)(2))(EtOH)(H2O)(3)] (3), and [(Mn3O)-O-III(Ph-sao)(3)(O2C-anthra)(MeOH)(4)]center dot Ph-saoH(2) (4 center dot Ph-saoH(2)) display dominant ferromagnetic exchange interactions leading to molecules with S = 6 ground states. The molecules are single molecule magnets (SMM) displaying large effective energy barriers for magnetization reversal. In each case their crystal structures reveal multiple intermolecular H-bonding interactions. Single crystal hysteresis loop measurements demonstrate that these interactions are strong enough to cause a clear field bias, but too weak to transform the spin networks into classical antiferromagnets. These three-dimensional networks of exchange coupled SMMs demonstrate that quantum tunnelling magnetization can be controlled using exchange interactions, suggesting supramolecular chemistry can be exploited to modulate the quantum physics of molecular magnets.