I would say that it depends on what exactly your city regulations are. There is a difference between a dog as a pet and a dog as a service animal. If the city laws state that only 3 pets are permitted per household, you should be able to keep all your four dogs, as one of them is (will be) a Psychiatric Service Dog. Service animals must be granted accommodation rights. I would recommend that you check the city regulations and consult the city council or a lawyer for accurate advice. According to ADA service dogs are subject to local animal control or public health requirements, as well as to local dog licensing and registration requirements. You can find more information on the ADA website here. Although mandatory registration or certification of service dogs is not permissible, it may be helpful if you can show such documentation as proof that the animal/animals (if you decide to train more than one) has/have gone through training. You can find some online courses with easy materials. i.e something like this one: PSD course, and then show the paper as proof. However, you may need to show a letter issued by your doctor so that you can verify that you actually need the dog/dogs as service animal/animals and they perform specific tasks for you. I hope that you will manage to keep all four dogs! :)