Lily Affinity in NG+

I’m nearing the end of my third playthrough, and am concerned by how difficult it was to get Lily’s affinity to 100%. After completing Abyss Levoire and both side quests that increase affinity, I still didn’t have enough, and only had a small handful of documents lying around that I could grab to raise it, and as far as I can tell, cans collected a second time in NG+ don’t give affinity. If I’m wrong, please correct me, but it seems like after you’ve collected every document, memory stick, and can, you’re just stuck being unable to unlock Eidos 9 in future playthroughs. Am I missing something?