The Greenland Ice Sheet (GrIS) has undergone accelerated ice-mass loss in recent decades and it is expected to be one of the main contributors to global sea-level rise in the coming century. Due to the existence of positive feedbacks governing its mass balance, it is thought to be a tipping element of the Earth system. Its stability has been studied under temperatures ranging from the present day to a global warming of +4 K, showing a threshold behavior leading to an ice-free state for warmer temperatures. However, its stability at lower temperatures has not been studied yet. Here we use the ice-sheet model Yelmo to obtain the stability diagram of the GrIS for the full range of glacial-interglacial temperatures, with regional summer air temperature anomalies relative to present extending from a climate representative of the Last Glacial Maximum (-12 K) to a warmer climate (+4 K). We find that the hysteresis persists in almost the entire studied range. Consistent with previous studies, a critical threshold is found between +1.2 and +1.8 K of regional summer air temperature anomaly, associated with atmospheric feedbacks that are represented by the coupled regional energy-moisture balance model REMBO. In addition, a second threshold is found for negative temperature anomalies, which is mainly driven by ocean warming that triggers the marine ice-sheet instability in the northeastern region of the glacial GrIS. The existence of this threshold is consistent with transient studies of the GrIS over the last glacial cycle.