Adding a furniture layer to the interior cubemapping function?

I’ve been working with the interior cubemapping node for a while and I love it, it’s fantastic. However one feature seems to be missing that is in other implementations of this which is a furniture layer to provide additional depth complexity. An example of this is shown here for Unity:

My instinct was simply to use a bumpoffset for the second layer and combine them with a lerp, this worked, kind of. There was noticeable shifting of the plane as the camera gets closer to glancing angles (no surprise here, bumpoffset always seems to have this issue) and walls from adjacent rooms do not occlude the objects.

I also tried opening up the function itself to see if I could figure out how it worked… but it is beyond my comprehension.

Hoping someone could give me some advice on how to achieve this?