No, you can have two. Mad had two, and I had two spiders at one time as well.
Buy one, put it in your house, go buy the other one. Once you put the second pet in the house or call the first out, they act the same a real $$ pets. Both go in or both come out.
Done deal!
I'll have two Boss Dragons to go please!

Now if you don't have a house - you are correct! And I agree with you, why not two shop pets?
Even if it's two different shop pets, for example a Bat and a Spider.
BUT a shop pet and a dog is better than one or the other.
EDIT: The MadTypist beat me to the punchline!