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Using observations of basal topography, ice thickness and modern accumulation rates, we use theory and a dynamic flowline model to examine the sensitivity of Antarctica's Foundation Ice Stream to changes in sea level, accumulation and buttressing at the grounding line. Our sensitivity studies demonstrate that the steep, upward-sloping basal topography inland from the grounding line serves to stabilize retreat of the ice stream, while the upward-sloping submarine topography downstream from the grounding line creates the potential for significant advance under conditions of modest sea-level lowering and/or increased accumulation rate. Extrapolating from Foundation Ice Stream, many nearby Weddell Sea sector ice streams are in a similar configuration, suggesting that the historical and projected responses of this sector's ice streams may contrast with those in the Amundsen or Ross Sea sectors. This work reaffirms that the greatest concerns for rapid West Antarctic Ice Sheet (WAIS) retreat are locations of reverse slopes, muted basal topography and limited lateral support.