We report on the magnetic properties of Eu2Ir2O7 upon the application of hydrostatic pressure P by means of macroscopic and local-probe techniques. In contrast to previously reported resistivity measurements, our dc magnetization data unambiguously demonstrate a non-monotonic P -dependence for TN , i. e., the critical transition temperature to the magnetic phase. More strikingly, we closely reproduce the recently calculated behaviour for TN under the assumption that P lowers the U/W ratio (i. e., Coulomb repulsion energy over electronic bandwidth). Zero-field muon-spin spectroscopy measurements confirm that the local magnetic configuration is only weakly perturbed by low P values, in agreement with theoretical predictions. The current results experimentally support the preservation of a 4-in/4-out ground state and, simultaneously, a departure from the single-band j eff = 1/2 model across the accessed region of the phase diagram.