There are dozens of albums I could say I know inside and out, but rather than list them all, I'm going to mention the first one that came to mind:
They Might Be Giants—Flood
Similar to what Duga said in the OP, in my early years of buying my own albums (junior high) I didn't own very many and thus listened to each one
a lot. Flood is one of the most extreme examples. I listened to this album so many times as a 13 and 14 year old that my dad once told me that he had gone from hating it to loving it through what I can only imagine was a Chinese water torture -esque experience in repetition for him. I can sing every word of this album, and I can't help but indulge that ability every time I listen to it, which happens surprisingly often for an album that I've owned for 22 years. It's actually sort of an internally underrated album for for me. It rarely springs to mind when I think of personal favorite or most influential recordings, but it surely deserves a place in the pantheon. It has heavily influenced my own songwriting in many subtle ways and is an album that I've never lost an interest in over all these years.