Is the space-time curvature linearly additive?

Could someone please show using equations if space-time curvature due to two bodies being linearly additive or not in general.

To see in a very concrete case that it is not additive, consider two spherically symmetric bodies centered at the same point. If you don't like them to overlap, take a ball and a spherical shell that doesn't intersect. Then at sufficient distance we have (wikipedia) that

$$R^{t}{}_{rrt} = \frac{r_s}{r^2(r_s-r)}$$

Since $$r_s$$ is linear in the masses, the curvature isn't.