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) relative to 2020, 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 [5, 95]% intervals of [0.3, 4.3]m and [1.0, 7.6]m under SSP1‐2.6 and SSP2‐4.5 respectively, and a difference in the 95% quantile of 1.6 m at 2300 and 3.3 m at 2500 for the two scenarios. The largest and most uncertain component is the Antarctic ice sheet, projected to contribute 5%–95% intervals of [−0.1, 2.3]m by 2500 under SSP1‐2.6 and [0.0, 3.8]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.