This paper describes the experiment protocol for coordinated simulations of Southern Ocean and combined dual-hemispheric (Southern Ocean and North Atlantic) ice sheet meltwater flux perturbations. These simulations form the second phase of the TIPMIP-OCEAN domain as part of the international Tipping Points Modelling Intercomparison Project (TIPMIP). We propose that the experiments are included in the Coupled Model Intercomparison Project Phase 7 (CMIP7), although any emission-driven Earth System Models can implement the protocol. The experimental design complements the first phase of the TIPMIP-OCEAN domain experiments which address the response of the North Atlantic to various amounts of Greenland Ice Sheet meltwater at different levels of global warming. Here we propose a similar protocol exploring the impact of freshwater fluxes from the Antarctic Ice Sheet into the Southern Ocean. Further, the impact of freshening in both hemispheres is examined, through simultaneous freshwater release around Greenland and off the coast of Antarctica. Together with the North Atlantic hosing simulations, our proposed experiments will assess the combined impact of freshening in both hemispheres on the stability of the Atlantic Meridional Overturning Circulation (AMOC) and Southern Ocean Abyssal Circulation (SOAC), and their associated potential tipping mechanisms and impacts on the Earth system.