LittleMsSam has a mod called MyPets that lets you have as many pets and horses as you want without adding them to your household. It's a great option for bigger families, unless you use a mod that makes your pets playable.
Unfortunately with bigger household sizes you have to temporarily remove a sim or pet from the family, then go into CAS, edit them, then add the sim or pet back into your family. I also had a problem where my game would crash sometimes when I tried to travel with a family larger than 8 Sims, so MyPets was a lifesaver for me.