She's six; any chance you can reduce the collection a little bit by having her choose some to give to kids who don't have any toys? With the holiday season approaching, that might be a tactic to try.

Otherwise, you will either need to add more storage or reduce the collection. Maybe add another hanging hammock--they are easy to put up and to take down and not as permanent as floating shelves.

Or maybe box some of the extras up for a month or two, to see if she misses them.

Or maybe give her a huge incentive to reduce the collection. Is there some toy/game that she really wants, but there isn't room for, because she has so many stuffed animals? Is she mature enough to understand that if she clears a certain amount of space, say the space taken up by 20 stuffed animals, there will be room for the thing she really wants?

My dd is 7. She doesn't like to give up stuffed animals either. Last year we got a puppy. He got into all of her stuffed animals and started playing with them. She was willing to let him have several. It helped weed out what she really didn't care about. You might see if she would be willing to donate the animals to an animal shelter or zoo or something. Let her get rid of everything she thinks the animals might like. Of course, not all stuffed animals are safe to pass on. It would at least give you the chance to see what is important to her so you can remove the rest.

My girls are 6 and 7 and both love stuffed animals and had way too many in their room. We implemented a "get 1=get rid of 2" plan. (Now if only I could do the same for some of my things.)