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Abstract Surface deformation plays a key role in illuminating magma transport at active volcanoes, however, unambiguous separation of deep and shallow transport remains elusive. The Socorro Magma Body (SMB) lacks an upper crustal magma transport system, allowing us to link geodetic measurements with predictions of numerical models investigating rheologic heterogeneities and magma‐mush interaction in the mid‐/lower crust. New InSAR observations confirm that a pattern of central surface uplift surrounded by a region of subsidence (previously coined “sombrero” deformation) has persisted over >100 years at the SMB. Our models suggest this pattern may reflect the presence of a large (>100 km width), weaker‐than‐ambient, compliant region (CR) surrounding the mid‐crustal magma body. Interactions between a pressurizing (e.g., due to melt injection and/or volatile exsolution) sill‐like magma body and CR drive the sombrero pattern, depending on both viscoelastic relaxation and pressurization timescales, explaining its rare observation and transient nature.