I think the likely answer is that it's one per shrine. I don't know if you can remove it once it's in.

[ Istredd crosses his arms and sighs, considering for a moment. ]

You and I have one. I think I counted four shrines so far. Two are open. Arguably, one of us could open the third and see what happens, and hold off on the last one. That doesn't make it safe, but it may be whatever she's warning about would happen as a last move.