Equivariant property (SI) revisited, II

We investigate Matui-Sato's notion of property (SI) for C*-dynamics, this time with a focus on actions of possibly non-amenable groups. The main result is a generalization of earlier work: For any countable group $\Gamma$ and any non-elementary separable simple nuclear C*-algebra $A$ with strict comparison, every amenable $\Gamma$-action on $A$ has equivariant property (SI). This is deduced from a more general statement involving relative property (SI) for certain inclusions into ultraproducts. The article concludes with a few consequences of this result.