This is absolutely correct.
We started with a cat. Or, should I say, I started with a cat when I moved to the city alone ten years ago.
We got a puppy many years later, and given that the cat was not so into playing, we figured puppy needed a friend--perhaps said friend could even bridge the gap between the two.
And so we got an outgoing kitten. Kitten (who is now over a year old) and puppy (who is now about three) are best friends. Kitten is also obsessed with cat and is a general pain in the ass, but it works.
We've reached a good number here. It's a good fit.
BUT there was a very sweet cat hanging out outside our house this past summer. He was obviously a stray. And man, I was tempted...
Perhaps thankfully, my landlord has made it clear that he does not want us to become a crazy cat couple, and knowing that has kept me somewhat on a leash.
