With a library card, most likely.
We were reading to my daughter when she was an infant and had no idea what was going on, every night, 2 to 3 books a night, and we carried that habit well into 4 or 5 years old, so I have no doubt we passed 1000 books. When she was older she had a few faves that we returned to, but mostly we were constantly getting new material
As for lending, I've have 55 books out right now. (Seattle area library system, son just turned 6) Sounds like you need to get to the library :)