<p>Irreversibly densified oxide glass under extreme deformation exhibits unexpected softening with plasticity, while the glass network typically becomes rigid as it densifies. These distinct mechanical responses in amorphous networks remain puzzling at the atomic level. Understanding this behavior requires knowledge of how the network entangles and connects under high pressure. Here, our measurements on densified amorphous oxides under irreversible densification via magnetic resonance spectroscopy provide evidence of enhanced network entanglement and, consequently, hyperconnectivity, as highlighted by an increase in highly coordinated Al’s and their spatial proximity. The results reveal that configurational diversity in prototypical amorphous Al₂O₃ under irreversible densification is more prominent than those of other complex oxide glasses, reaching hyperconnected under much lower pressures. In general, attainment of configurational diversity at lower pressures is promoted by increasing field strength of non-network cations in glasses under irreversible densification. The enhanced connectivity with increasing densification allows us to postulate the origin of mechanical responses in glass networks. Particularly, attainment of hyperconnectivity under lower pressures may promote network flexibility during deformation. This conceptual protocol enables control of dual mechanical responses in glasses under extreme stress, guiding the discovery of super-hard densified glasses for technological innovation and accounting for the weakening of hyperconnected glasses in planetary interiors.</p>