Sheep, Alice and Claudio
When I was part owner of a ranch outside of San Miguel de Allende in Mexico, we had a herd of Dorper, Peleway and Black Belly sheep, plus rabbits, chickens, and quail. None of them exotic, but not exactly household pets either.
Most people have dogs or cats as house pets, but we had a rabbit and a rooster that ran freely in our San Miguel home! Alice, the rabbit, would frequently pass through the bedroom on one of her explorations. Claudio, the rooster, would perch on the back of the sofa during cocktail hour begging for peanuts. Fortunately, Claudio was house broken to the point where he would only do his business in the garden. I love the crow of a rooster at the break of dawn, but some of our guests did not appreciate the crowing. So, in those cases, Carlos, the house man, would have to put Claudio in the garage at night.