The Southern Ocean is critically important to the oceanic uptake of anthropogenic CO2. Up to half of the excess CO2 currently in the ocean entered through the Southern Ocean. That uptake helps to maintain the global carbon balance and buffers transient climate change from fossil fuel emissions. However, the future evolution of the uptake is uncertain, because our understanding of the dynamics that govern the Southern Ocean CO2 uptake is incomplete. Sparse observations and incomplete model formulations limit our ability to constrain the monthly and annual uptake, interannual variability and long-term trends. Float-based sampling of ocean biogeochemistry provides an opportunity for transforming our understanding of the Southern Ocean CO2 flux. In this work, we review current estimates of the CO2 uptake in the Southern Ocean and projections of its response to climate change. We then show, via an observational system simulation experiment, that float-based sampling provides a significant opportunity for measuring the mean fluxes and monitoring the mean uptake over decadal scales.