  Let $A_\Gamma$ be an Artin group with defining graph $\Gamma$. We introduce
the notion of $A_\Gamma$ being extra-large relative to a family of arbitrary
parabolic subgroups. This generalizes a related notion of $A_\Gamma$ being
extra-large relative to two parabolic subgroups, one of which is always large
type. Under this new condition, we show that $A_\Gamma$ satisfies the
$K(\pi,1)$ conjecture whenever each of the distinguished subgroups do. In
addition, we show that $A_\Gamma$ is acylindrically hyperbolic under only mild
conditions.
