Yes, you can get organized.
If books are being read, you'll have to be flexible about your organization system. The picture you see above is a day of returning books to the basement. I'm organized but not too organized. Take what you can from how I try to stay organized. Everyone has to come up with a system that works for their own family.
We keep a tub for public library books on the bottom shelf of a bookcase in our livingroom.
My children have a box of books next to their beds. We just went through the boxes a few days ago. They searched our collection of books in the basement and went through some books I purchased at a used book store to add new ones to their boxes. They kept some of their favorites for rereading. When they were younger most of the books were ones we read together once, and they reread for practice. They all seem to like reading new books now. Rereading books helped my children become fluent readers and improve decoding skills.
These are the books my children chose for their boxes recently.