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 ∼80 cm to ∼150 cm. Revised median RSL projections would, without protective measures, by 2100 submerge land currently home to >79 million people, an increase of ∼25 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 ∼900 million people (vs. ∼80 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.