© 2016 American Physical Society. Background: Competing interpretations of the results of a Mg30(t,p)Mg32 measurement populating the ground state and 02+ state in Mg32, both limited to a two-state mixing description, have left an open question regarding the nature of the Mg32 ground state. Purpose: Inspired by recent shell-model calculations, we explore the possibility of a consistent interpretation of the available data for the low-lying 0+ states in Mg32 by expanding the description from two-level to three-level mixing. Methods: A phenomenological three-level mixing model of unperturbed 0p0h, 2p2h, and 4p4h states is applied to describe both the excitation energies in Mg32 and the transfer reaction cross sections. Results: Within this approach, self-consistent solutions exist that provide good agreement with the available experimental information obtained from the Mg30(t,p)Mg32 reaction. Conclusion: The inclusion of the third state, namely the 4p4h configuration, resolves the "puzzle" that results from a two-levelmodel interpretation of the same data. In our analysis, the Mg32 ground state emerges naturally as dominated by intruder (2p2h and 4p4h) configurations, at the 95% level.