You can get those grids at Walmart (if your store doesn’t carry them, you can buy online and ship free to store) or at Sears! I have used them for years and I just attach with zip ties. I have also picked some up at thrift stores.
I am redoing my cage right now, too. My cage currently is three levels. I used the grids, but first, I cut “bunny” doors using wire cutters (I have a house kitty, too, so it is a spot JUST for my bunny that the cat can’t get into). The way I am setting it up now will have a little area in the back for his bed and supplies (kind of like a backyard). I did have to use some cheap plastic placemats to cover some of the grates so my cat wouldn’t reach inside. With this setup, Barnaby bunny has his own condo, backyard, but can hang out with me and my cat Loki when he wants. He still enjoys sleeping on my bed with me.
One thing you can do that she’ll likely appreciate is having the cage be her area. With Barnaby, unless I am cleaning his litterbox or feeding him, I don’t invade his space. In return, he doesn’t poop in mine, haha. 

