A circular polarizing filter is simply a linear polarizing filter plus a quarter-wave plate. The linear filter does all the photographic work (darkening skies, cutting through reflections). The quarter-wave plate is there only to convert the linearly polarized light transmitted by the first filter into circularly polarized light, which can then pass through the beamsplitter and AF system of a modern camera.
If you stack a linear polarizer on top of the circular polarizer, then the new linear polarizer does all the photographic work, the second linear polarizer blocks a variable fraction of the light passing through the first polarizer, and the quarter-wave plate again produces circularly polarized light. If the two linear polarizers are parallel, the second one does nothing; if the two linear polarizers are crossed, the second one blocks nearly all of the light transmitted by the first one.
If you have followed all of this, here is a quiz: why would it not work to stack the circular polarizer on top of the linear polarizer?