Once any potential gaps in the wall from constructing a new frame are filled, drill holes in the top and bottom of the secret bookcase door around one-third of the way for your center pivot hinges ...

Of course, then your bookcase would have to be wider, but that might not be so awful. Bonus: If you wanted, you could swivel it around to have the opposite side face outward.

Hidden Doors by Design, LLC™, which creates award-winning hidden door bookcases and cabinets, recently unveiled and installed a new door.Its 180-degree hidden door, US patent number 9,598,887 B2, ...

Bookcase-fronted doors leading to hidden stairs at the Morgan Library & Museum in New York City. ... And then there are the D.I.Y.ers who just like geeking out on things like pivot hinges.