The effect of replacing magnesia by alumina on the pressure-dependent structure of amorphous enstatite was investigated by applying in situ high-pressure neutron diffraction with magnesium isotope substitution to glassy (MgO)0.375(Al2O3)0.125(SiO2)0.5. The replacement leads to a factor of 2.4 increase in the rate-of-change of the Mg–O coordination number with pressure, which increases from 4.76(4) at ambient pressure to 6.51(4) at 8.2 GPa, and accompanies a larger probability of magnesium finding bridging oxygen atoms as nearest-neighbors. The Al–O coordination number increases from 4.17(7) to 5.24(8) over the same pressure interval at a rate that increases when the pressure is above ∼3.5 GPa. On recovering the glass to ambient conditions, the Mg–O and Al–O coordination numbers reduce to 5.32(4) and 4.42(6), respectively. The Al–O value is in accordance with the results from solid-state 27Al nuclear magnetic resonance spectroscopy, which show the presence of six-coordinated aluminum species that are absent in the uncompressed material. These findings explain the appearance of distinct pressure-dependent structural transformation regimes in the preparation of permanently densified magnesium aluminosilicate glasses. They also indicate an anomalous minimum in the pressure dependence of the bulk modulus with an onset that suggests a pressure-dependent threshold for transitioning between scratch-resistant and crack-resistant material properties.