We prove that if g and n are integers at least two, then the abstract commensurator of the braid group with n strands on a closed orientable surface of genus g is naturally isomorphic to the extended mapping class group of a compact orientable surface of genus g with n boundary components.
"Commensurators of surface braid groups." J. Math. Soc. Japan 63 (4) 1391 - 1435, October, 2011. https://doi.org/10.2969/jmsj/06341391