Probabilistic sea-level projections have not yet integrated insights from physical ice-sheet models representing mechanisms, such as ice-shelf hydrofracturing and ice-cliff collapse, that can rapidly increase ice-sheet discharge. Here, we link a probabilistic framework for sea-level projections to a small ensemble of Antarctic ice-sheet (AIS) simulations incorporating these physical processes to explore their influence on projections of global-mean sea-level (GMSL) and relative sea-level (RSL) change. Under high greenhouse gas emissions (Representative Concentration Pathway [RCP] 8.5), these physical processes increase median projected 21st century GMSL rise from \(\sim80\) cm to \(\sim150\) cm. Revised median RSL projections would, without protective measures, by 2100 submerge land currently home to \(>79\) million people, an increase of \(\sim25\) million people. The use of a physical model, rather than simple parameterizations assuming constant acceleration, increases sensitivity to forcing: overlap between the central 90\% of the frequency distributions for 2100 for RCP 8.5 (93--243 cm) and RCP 2.6 (26--98 cm) is minimal. By 2300, the gap between median GMSL estimates for RCP 8.5 and RCP 2.6 reaches \(>10\) m, with median RSL projections for RCP 8.5 jeopardizing land now occupied by \(\sim900\) million people (vs. \(\sim80\) million for RCP 2.6). There is little correlation between the contribution of AIS to GMSL by 2050 and that in 2100 and beyond, so current sea-level observations cannot exclude future extreme outcomes. These initial explorations indicate the value and challenges of developing truly probabilistic sea-level rise projections incorporating complex ice-sheet physics.