Welcome to the EF, I think it is really cool that you have so many pets, I wish! Unfortunately, I believe that so many pets would need a house and not an appartment. SO maybe for you it would be probably better if you rented outside the city in Basel Stadt (but still pretty close to the city).
Usually finding a place for cats (usually a couple of them) is not a problem but 9 cats would not be a common number (although I am loving the idea

) and dogs, it is not so easy...
Good luck!
Angela