intersecting *semi-riemannian* manifolds

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I read this interesting post: Intersection of manifolds.

In geometry/topology one can consider intersection of manifolds (which need not be a manifold). I'm curious if one can do this in Semi-Riemannian geometry in a meaningful way?

Specifically I guess:

Has anyone ever studied in general, the problem of $k$ intersecting solutions to the EFE with cosmological constants?

And is there any motivation to study this?

Some extra conditions may be that the resulting structure is again a solution to the EFE. I think one would unfortunately have to drop the property of causality.