The widespread High Arctic Large Igneous Province (HALIP) exhibits prolonged melting over more than 50 Myr, an observation that is difficult to reconcile with the classic view of large igneous provinces and associated melting in plume heads. Hence, the suggested plume-related origin and classification of HALIP as a large igneous province have been questioned. Here, we use numerical models that include melting and melt migration to investigate a rising plume interacting with variable lithosphere thickness, i.e. an extended-basin-to-craton setting. Models reveal significant spatial and temporal variations in melt volumes and pulses of melt production, including protracted melting for at least about 30-40 Myr, but only if migrating melt transports heat upwards and enhances local lithospheric thinning. Plume material deflected from underneath the Greenland craton can then re-activate melting zones below the previously plume-influenced Sverdrup Basin, even though the plume is already ~500 km away. Hence, melting zones may not represent the location of the deeper plume stem at a given time. Plume flux pulses associated with mantle processes or magma processes within the crust may alter the timing and volume of secondary pulses and their surface expression. Our models suggest that HALIP magmatism is expected to exhibit plume-related trace element signatures throughout time, but potentially shift from mostly tholeiitic magmas in the first pulse towards more alkalic compositions for secondary pulses, with regional variations in timing of magma types. We propose that the prolonged period of rejuvenated magmatism of HALIP is consistent with plume impingement on a cratonic edge.