Many people have multiple pets. A "precious pets" is one or more particular pets doted upon in a oft excessive manner so as to resemble the parent child relationship in humans. The pet owner's behavior may be marked by excessive attention to the pet, excessive concern over the comfort and welfare of the pet, or tolerance of otherwise unacceptable actions by the pet.
Kirk has several pythons but the ferret, which he calls his baby, is his precious pet.
Jane lets Rocky destroy her home because he is her precious pet.