Zach, Andy,
My understanding is that you can stack them, with a five or six millimetre plastic/timber spacer between them, but there's one proviso.
You must not put a completed metallic circuit from the inside right around the outside. This would create another secondary, with one turn.
So, if you have a very long bolt extending up through the center, it must not be supported at the top with a metallic bracket, as this would complete the circuit with the base attachment.
Hope this helps,
Cheers,
Hugh