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

The $K(\pi,1)$ conjecture and acylindrical hyperbolicity for relatively extra-large Artin groups