  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.
