Couple of things.
I would look for an older pup. Your dog sounds too rambunctious for a baby
Look into a rescue group. A Labrador or Golden would be a nice match.
Next. Don't let your dog bully another dog. Just because he wants to neck grab and body slam a dog into a TV stand, does not mean you have to let him. It's up to you to protect whatever new dog you bring into the family and not let them be terrorized by the current resident. It's very unfair to the new and probably already scared dog. Same goes for the cats. Your dog is getting bloodied from their attempts to fend him off. He needs to learn some manners. That's your job. Not the cats or other dogs.
If he is being overwhelming, put him in a time out. Take him away from the situation, do obedience commands with him. Make him behave. Don't just expect another animal to put up with him or enjoy everything he throws out. Each animal is different. We have to respect that about each if them if we want them to live harmoniously.
Good luck with your search!!!
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