  Using limit linear series on chains of curves, we show that closures of
certain Brill-Noether loci contain a product of pointed Brill-Noether loci of
small codimension. As a result, we obtain new non-containments of Brill-Noether
loci, in particular that dimensionally expected non-containments hold for
expected maximal Brill-Noether loci. Using these degenerations, we also give a
new proof that Brill-Noether loci with expected codimension $-\rho\leq \lceil
g/2 \rceil$ have a component of the expected dimension. Additionally, we obtain
new non-containments of Brill-Noether loci by considering the locus of the
source curves of unramified double covers.
