Climate variations cause ice sheets to retreat and advance, raising or lowering sea level by metres to decametres. The basic relationship is unambiguous, but the timing, magnitude and sources of sea-level change remain unclear; in particular, the contribution of the East Antarctic Ice Sheet (EAIS) is ill defined, restricting our appreciation of potential future change. Several lines of evidence suggest possible collapse of the Totten Glacier into interior basins during past warm periods, most notably the Pliocene epoch, causing several metres of sea-level rise. However, the structure and long-term evolution of the ice sheet in this region have been understood insufficiently to constrain past ice-sheet extents. Here we show that deep ice-sheet erosion-enough to expose basement rocks-has occurred in two regions: the head of the Totten Glacier, within 150 kilometres of today's grounding line; and deep within the Sabrina Subglacial Basin, 350-550 kilometres from this grounding line. Our results, based on ICECAP aerogeophysical data, demarcate the marginal zones of two distinct quasi-stable EAIS configurations, corresponding to the 'modern-scale' ice sheet (with a marginal zone near the present ice-sheet margin) and the retreated ice sheet (with the marginal zone located far inland). The transitional region of 200-250 kilometres in width is less eroded, suggesting shorter-lived exposure to eroding conditions during repeated retreat-advance events, which are probably driven by ocean-forced instabilities. Representative ice-sheet models indicate that the global sea-level increase resulting from retreat in this sector can be up to 0.9 metres in the modern-scale configuration, and exceeds 2 metres in the retreated configuration.