  We establish $\mathcal{Z}$-stability for crossed products of outer actions of
amenable groups on $\mathcal{Z}$-stable $C^*$-algebras under a mild technical
assumption which we call McDuff property with respect to invariant traces. We
obtain such result using a weak form of dynamical comparison, which we verify
in great generality. We complement our results by proving that McDuffness with
respect to invariant traces is automatic in many cases of interest. This is the
case, for instance, for every action of an amenable group $G$ on a classifiable
$C^*$-algebra $A$ whose trace space $T(A)$ is a Bauer simplex with finite
dimensional boundary $\partial_e T(A)$, and such that the induced action
$G\curvearrowright \partial_eT(A)$ is free. If $G = \mathbb{Z}^d$ and the
action $G\curvearrowright \partial_eT(A)$ is free and minimal, then we obtain
McDuffness with respect to invariant traces, and thus $\mathcal{Z}$-stability
of the corresponding crossed product, also in case $\partial_e T(A)$ has
infinite covering dimension.
