  In this paper we prove homological stability for certain subgroups of surface
braid groups. Alternatively, this is equivalent to proving homological
stability for configurations of subsets of exactly $\xi$ points in a surface as
we increase the number of subsets. For open surfaces, we prove the result
integrally using a variation of the arc complex which we dub the "fern
complex". We use a technique of Randal-Williams to extend the result rationally
for closed surfaces.
