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 that large igneous provinces (LIPs) originate from melting in plume heads. Hence, the suggested plume‐related origin and classification of HALIP as a LIP have been questioned. Here, we use numerical models that include melting and melt migration to investigate a rising plume interacting with lithosphere of variable thickness, that is, a basin‐to‐craton setting applicable to the Arctic. Models reveal that melt migration introduces significant spatial and temporal variations in melt volumes and pulses of melt production, including protracted melting for at least about 30–40 Myr, because of the dynamic feedback between migrating melt and local lithosphere thinning. For HALIP, plume material deflected from underneath the Greenland craton can re‐activate melting zones below the previously plume‐influenced Sverdrup Basin after a melt‐free period of about 10–15 Myr, even though the plume is already ∼500 km away. Hence, actively melting zones do not necessarily represent the location of the deeper plume stem at a given time, especially for secondary pulses. Additional processes such as (minor) plume flux variations or local lithospheric extension may alter the timing and volume of HALIP pulses, but are to first order not required to reproduce the long‐lived and multi‐pulse magmatism of HALIP. Since melting zones are always plume‐fed, we would expect HALIP magmatism to exhibit plume‐related trace element signatures throughout time, potentially shifting from mostly tholeiitic toward more alkalic compositions.