Situated in the so-called “island of inversion,” the nucleus ³²Mg is considered as an archetypal example of the disappearance of magicity at $N=20$. We report on high statistics in-beam spectroscopy of ³²Mg with a unique approach, in that two direct reaction probes with different sensitivities to the underlying nuclear structure are employed at the same time. More specifically, states in ³²Mg were populated by knockout reactions starting from ³³Mg and ³⁴Si, lying inside and outside the island of inversion, respectively. The momentum distributions of the reaction residues and the cross sections leading to the individual final states were confronted with eikonal-based reaction calculations, yielding a significantly updated level scheme for ³²Mg and spin-parity assignments. By fully exploiting observables obtained in this measurement, a variety of structures coexisting in ³²Mg was unraveled. Comparisons with theoretical predictions based on shell-model overlaps allowed for clear discrimination between different structural models, revealing that the complete theoretical description of this key nucleus is yet to be achieved.