The dynamics of the ice sheets on glacial-interglacial time scales are highly controlled by interactions with the solid Earth, i.e., glacial isostatic adjustment (GIA). Particularly at marine ice sheets, competing feedback mechanisms govern the migration of the ice sheet's grounding line and hence the ice sheet stability. In this study, we run coupled ice sheet–solid Earth simulations over the last two glacial cycles. For the ice sheet dynamics we apply the Parallel Ice Sheet Model PISM and for the load response of the solid Earth we use the three-dimensional viscoelastic Earth model VILMA, which, in addition, considers the gravitationally consistent redistribution of water (the sea level equation). We decided on an offline coupling between the two model components. By convergence of trajectories of the Antarctic Ice Sheet deglaciation we determine optimal coupling time step and spatial resolution and compare patterns of inferred relative sea level change since the Last Glacial Maximum with the results from previous studies. With our coupling setup we evaluate the relevance of feedback mechanisms for the glaciation and deglaciation phases in Antarctica considering different 3D Earth structures resulting in a range of load-response time scales. For rather long time scales, in a glacial climate associated with far-field sea level low stand, we find grounding line advance up to the edge of the continental shelf mainly in West Antarctica, dominated by a self-amplifying GIA feedback, which we call the `forebulge feedback'. For the much shorter time scale of deglaciation, dominated by the Marine Ice Sheet Instability, our simulations suggest that the stabilizing GIA feedback can significantly slow-down grounding line retreat in the Ross sector, which is dominated by a very weak Earth structure (i.e. low mantle viscosity and thin lithosphere). This delaying effect prevents a Holocene grounding line retreat beyond its present-day location, which is discussed in the scientific community, supported by observational evidence at the Siple Coast and by previous model simulations.  The described coupled framework, PISM-VILMA, allows for defining restart states to run multiple sensitivity simulations from. It can be easily implemented in Earth System Models (ESMs) and provides the tools to gain a better understanding of ice sheet stability on glacial time scales as well as in a warmer future climate.