Extensions of multicurve stabilizers are hierarchically hyperbolic

For a closed and orientable surface S with genus at least 2, we prove that the 1 .S /-extensions of the stabilizers of multicurves on S are hierarchically hyperbolic groups.This answers a question of Durham, Dowdall, Leininger and Sisto.We also include an appendix that employs work of Charney, Cordes and Sisto to characterize the Morse boundaries of hierarchically hyperbolic groups whose largest acylindrical action on a hyperbolic space is on a quasitree.