Marine ice, sometimes as part of an ice mélange, significantly affects ice shelf flow and ice fracture. The highly heterogeneous structure of the Brunt/Stancomb-Wills Ice Shelf (BSW) system in the east Weddell Sea offers a rare setting for uncovering the difference in rheology between meteoric and marine ice. Here, we use data assimilation to infer the rheology of the Brunt/Stancomb-Wills Ice Shelf by an inverse control method that combines interferometric synthetic aperture radar measurements with numerical modeling. We then apply the inferred rheology to support the hypothesis attributing the observed 1970s ice shelf flow acceleration to a change in the stiffness of the ice mélange area connecting Brunt proper with Stancomb-Wills and to examine the consequences of frontal rift propagation. We conclude that while the Brunt/Stancomb-Wills system is currently not susceptible to extreme fragmentation similar to that of the Larsen B Ice Shelf in 2002, our inverse and forward modeling results emphasize its vulnerability to destabilization by relatively rapid changes in the ice mélange properties, resulting from the interaction of its marine ice component with ocean water, or by the further propagation of a frontal rift.