PtPT: 1 opens one minor option in the Nadir, one option if you’re Seeking, and one option at Hallowmass. Unless there’s something Fate-locked I don’t know about, those are its only uses, but because it’s tricky to get, some late-game players try to get it to 3 (the highest possible level.)
I have “Putting the Pieces Together: The Drownies” at 3 (check my profile; it’s up on my Scrapbook), but I don’t recall how I got it there. I have nothing to add about its uses other than what Greg M said.