Normally we wouldn't stack two noun modifiers together like that, regardless of whether "which" or "that" is used. In this case, since the first modifier ends in a noun ("interior"), the second modifier ends up incorrectly modifying that noun. That's one of the main reasons we're not going to do well stacking modifiers.
In theory, you could have two modifiers, one essential (using that) and the other non-essential (using which):
The book that I wrote, which comes out this
...
In theory, you could have two modifiers, one essential (using that) and the other non-essential (using which):
The book that I wrote, which comes out this
...
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