The only animal I’ve seen take down squirrels besides dogs and cats (cats don’t usually kill enough) are foxes, although I’m sure coyotes do as well. A momma fox can clean out quite a few quickly and sometimes bring control.
That said, I protect hundreds of trees from squirrels affectively with my squirrel baffles and have often mentioned it here and yet somehow it hasn’t been widely adopted by members of this forum and I wonder why. Hell, I have a next door neighbor whose never seen baffles on my property (I don’t use them for my orchard for a couple of reasons) that is using them on his property- I don’t even know how he learned about them.
30 years ago when I started trying to protect fruit against grey squirrels here all I saw used in my area that was similar was duct pipe, which works well but is a pain to install and pretty expensive. I’m sure I’m not the first one to think of using roofing coil stapled into the trunks of trees that are trained to have no branches below 5’ of straight trunk, but I bet I’ve protected more trees for more seasons with the method than anyone you are likely to meet.
At some point I started painting them with a mixture of axel grease and motor oil so they can’t muscle there way up them. DIY Squirrel Baffle ideas? - #24 by alan