Polynuclear single-molecule magnets (SMMs) were diluted in a diamagnetic crystal lattice to afford arrays of independent and iso-oriented magnetic units. Crystalline solid solutions of an Fe(4) SMM and its Ga(4) analogue were prepared with no metal scrambling for Fe(4) molar fractions x down to 0.01. According to high-frequency EPR and magnetic measurements, the guest SMM species have the same total spin (S=5), anisotropy, and high-temperature spin dynamics found in the pure Fe(4) phase. However, suppression of intermolecular magnetic interactions affects magnetic relaxation at low temperature (40 mK), where quantum tunneling (QT) of the magnetization dominates. When a magnetic field is applied along the easy magnetic axis, both pure and diluted (x=0.01) phases display pronounced steps at evenly spaced field values in their hysteresis loops due to resonant QT. The pure Fe(4) phase exhibits additional steps which are firmly ascribed to two-molecule QT transitions. Studies on the field-dependent relaxation rate showed that the zero-field resonance sharpens by a factor of five and shifts from about 8 mT to exactly zero field on dilution, in agreement with the calculated variation of dipolar interactions. The tunneling efficiency also changes significantly as a function of Fe(4) concentration: the zero-field resonance is significantly enhanced on dilution, while tunneling at ±0.45 T becomes less efficient. These changes were rationalized on the basis of a dipolar shuffling mechanism and transverse dipolar fields, whose effect was analyzed by using a multispin model. Our findings directly prove the impact of intermolecular magnetic couplings on SMM behavior and disclose the magnetic response of truly isolated giant spins in a diamagnetic crystalline environment.