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Future sea-level rise projections are characterized by both quantifiable uncertainty and unquantifiable structural uncertainty. Thorough scientific assessment of sea-level rise projections requires analysis of both dimensions of uncertainty. Probabilistic sea-level rise projections evaluate the quantifiable dimension of uncertainty; comparison of alternative probabilistic methods provides an indication of structural uncertainty. Here we describe the Framework for Assessing Changes To Sea-level (FACTS), a modular platform for characterizing different probability distributions for the drivers of sea-level change and their consequences for global mean, regional, and extreme sea-level change. We demonstrate its application by generating seven alternative probability distributions under multiple emissions scenarios for both future global mean sea-level change and future relative and extreme sea-level change at New York City. These distributions, closely aligned with those presented in the Intergovernmental Panel on Climate Change Sixth Assessment Report, emphasize the role of the Antarctic and Greenland ice sheets as drivers of structural uncertainty in sea-level change projections.