Self-grooming ideas for dog

This is an odd question, but my dog adores our (fake) Christmas tree—he sits and hides under it, and will always intentionally walks under it when he’s near it. I like to think he’s scratching his back with the little branches… He also loves to rub and nuzzle against the couch almost like a cat.

Since I can’t leave the tree up all year, I was wondering if anyone has ideas of what I can put out in place of the tree so he can live out his back-scratching dreams for the other 10 months of the year?

I was looking into those cat grooming arches, but I can’t find one big enough with good reviews, and I can already imagine him knocking it over. I’ve also seen people attach brushes to furniture somewhat like the grooming brushes for livestock, but he wouldn’t be able to get his back!

Thanks in advance for any recommendations!