I would do some kind of enclosed storage, or even one of those “beanbag stuffed animal storage” things. stuffed animals can get pretty dusty when piled up in a net/hammock. I also think it ok to sit down with him and start to downsize his collection. Find a number you are comfortable with, and rehome the rest (and limit any new ones coming in!)

I have 3 kiddos (10,8 and 6), and I have issues with stuffed animals, haha. The most they have ever had at one time is 3 each......one to sleep with and two special ones to play with. Most of the time the “play with” ones just sit in the basket we store them in. If they want a new stuffie (which has only happened a few times), they need to let one go before they bring a new one home. My family knows not to gift any stuffies for birthdays or Christmas, too, ;-)

We used large fabric laundry hampers (open top). The ones meant for corners work well in a closet. My husbands trick was to talk the kids into packing some away in the attic. They would forget about them, and he would donate them (if they were decent) or toss them. My 17 year old son still has a basket in his room. I’m not sure what he’s saving them for.