YOu could loosen, but not remove the comode. What you want to do it to slide a shim like a 4x4 ceramic tile in the back to tilt the works up just a bit to allow for 1/4 inch wain to fit behind.
I would also venture to bet that if you carefully grabed the tank of the comode and pulled forward just a bit, you could slide 1/4 ply in that area.
Do not force anything.
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