We produce projections of global mean sea-level rise to 2500 for low and medium emissions scenarios (Shared Socioeconomic Pathways SSP1-2.6 and SSP2-4.5), based on extending and combining model ensemble data from current literature. We find that emissions have a large effect on sea-level rise on these long timescales, with a difference of 0.95 m at 2300 and 1.40 m at 2500 between the medians for the two scenarios. The largest and most uncertain component is the Antarctic ice sheet, projected to contribute median and 5-95% intervals of 0.86 [0.40, 1.57] m by 2500 under SSP1-2.6 and 1.44 [0.68, 2.71] m under SSP2-4.5. We discuss how the simple statistical extensions used here could be replaced with more physically-based methods for more robust predictions. We show that, despite their uncertainties, current multi-centennial projections combined into multi-study projections as presented here can be used to avoid future ‘lock-ins’ in terms of risk and adaptation needs to sea-level rise.