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Understanding the potential future evolution of the Greenland Ice Sheet (GrIS) is of critical importance for anticipating the consequences of global climate change. GrIS melt contributes between 0.5-0.8 mm per year to total global sea level rise and the total ice volume has the potential to raise sea levels by 7 meters. Furthermore, freshwater delivery to the North Atlantic has important implications for the stability of the density-driven Atlantic Meridional Overturning Circulation. A critical challenge in anticipating GrIS sea level rise contribution and North Atlantic freshwater delivery arises from the so-called inertia of the ice sheet, wherein present-day and near-term future warming may trigger ice loss that unfolds on century to millennial timescales. The GrIS is considered one of the Earth system’s tipping elements, components of the Earth system wherein crossing a critical global warming threshold leads to large-scale and nonlinear change in system state. Though it is subject to a number of self-amplifying (and -dampening) feedbacks, the susceptibility of the GrIS to tipping is not well-constrained, with particular uncertainties arising over long (1-10 kyr) timescales, given different global warming rates, and under potential scenarios of “stabilised” or landing climate (i.e., the Paris-agreed 1.5 C). The Tipping Points Modelling Intercomparison Project (TIPMIP) seeks to investigate the likelihood, impacts, and risk of crossing Earth system tipping points in so-called global tipping elements—components which, if tipped, have widespread consequences for the whole Earth system. Here we present initial explorations of the response of the GrIS to the transient, idealised warming scenarios following the TIPMIP-ESM and TIPMIP-ICESHEET domain protocols, with standalone, offline experiments undertaken using the Parallel Ice Sheet Model (PISM). These idealised warming scenarios have been designed to explore both the warming-induced triggers of tipping dynamics as well as their feedbacks over century to millennia timescales.