The cage protrudes on the side without the handle
and prevents LA-EA4 adapters from being mounted to the camera.
I’ve tested this with my actual products.
It might be possible to attach the cage to the ZV-E10 with an LA-EA4 adapter already mounted,
since the cage also protrudes on the bottom side,
but not as much.
However, I haven’t tried this yet.
The same issue should also apply to LA-EA2 adapters.