  We study the restriction of Brill-Noether loci to the gonality stratification
of the moduli space of curves of fixed genus. As an application, we give new
proofs that Brill-Noether loci with $\rho=-1$ have distinct support, and for
fixed $r$ give lower bounds on when one direction of the non-containments of
the Maximal Brill-Noether Loci Conjecture hold for Brill-Noether loci of rank
$r$ linear systems. Using these techniques, we also show that Brill-Noether
loci corresponding to rank $2$ linear systems are maximal as soon as $g\ge 28$
and prove the Maximal Brill-Noether Loci Conjecture for $g=20$.
