First, you may want to consider your dog's nature. If your beloved pet is a bit of a bully and the new dog isn't submissive, there are going to be some major battles before they sort out which dog is in charge. Sometimes, two dogs are equally dominant and these battles flare up again and again. By the time you visit your veterinarian for the fourth or fifth time to have their battle scars treated, you may be regretting the purchase of a second dog.