Ice discharge from the Antarctic Ice Sheet into the Southern Ocean has been increasing in recent decades and is expected to continue increasing in the future. Additionally, incursions of Circumpolar Deep Water onto the continental shelf have the potential to trigger order of magnitude increases in melt through ice-shelf melt regime changes. Changes in freshwater flux significantly affect the ocean temperature and salinity on the continental shelf and have been shown to cause recent changes in local steric sea level of a few mm per year. Here we investigate how changes in magnitude and distribution of ice-sheet freshwater fluxes alter patterns of steric sea level on the Antarctic continental shelf using simulations from the Energy Exascale Earth System Model (E3SM). First we compare steric sea level patterns in E3SM simulations that include realistic distributions of ice-shelf and iceberg meltwater against simulations that use a more simplistic distribution of Antarctic freshwater flux applied at the sea surface uniformly along the coast. We also investigate steric sea level changes due to incursions of warm, salty Circumpolar Deep Water onto the continental shelf in the southern Weddell Sea and the sea level changes due to a subsequent ice-shelf melt regime shift to order-of-magnitude higher melt rates beneath the Filchner-Ronne Ice Shelf. These changes can alter local steric sea level by several mm. Finally, for context, we compare the steric sea level change from these two scenarios with ocean dynamic sea level differences and local sea level changes due to gravitational and rotational changes associated with recent and projected Antarctic Ice Sheet mass loss. Results suggest freshwater variations in the coastal Southern Ocean can have a significant impact on local sea level, though likely not enough to significantly alter ocean, ice sheet, or sea ice dynamics.