Basal melting of Antarctic Ice Shelves is thought to be a key process in the future evolution of the Antarctic Ice Sheet and large-scale ocean circulation. Observations show that most ice shelves in West Antarctica are melting rapidly, while for the two largest ice shelves, the Filchner--Ronne and Ross Ice Shelf (FRIS and RIS), melt rates are still relatively low, implying the potential threat of accelerated mass loss in the future. By prescribing freshwater forcing projected by ice sheet models, previous studies emphasize the essential and complex role of ice-shelf meltwater for future climates, including an abyssal ocean overturning slowdown, sea ice expansion and global warming reduction. However as yet, only very few model approaches have taken an explicit simulation of ice-shelf cavities into account. Here we implement Antarctic ice-shelf cavities into a complex state-of-the-art multi-scale Earth system model to investigate the responses and feedbacks of ice-shelf basal melting in climate projections. We find that a combination of regional hydrography and topography dominantly determines the existence of a tipping point. At this point warm water intrudes the FRIS-cavity intensely, which causes a rapid increase in the melting rate and freshwater release in response to increasing CO2 levels already within this century. In contrast, a more gradual response is simulated for the RIS. However, despite a possible FRIS instability, our results suggest that previous ice sheet modelling and freshwater experiments have overestimated future ice shelf melt. Hence, comprehensive model approaches, including both interactive ice sheets and their cavities, represent an urgent need for an enhanced assessment of the combined effects in climate projections.