Similar Evolution

What if most of the animal species evolved alongside humans in a similar fashion?

It's common for fiction, especially in animation, to replace humans with mostly bipedal human-like animals. A walking and talking mouse that wears clothes for instance. What if we twisted that concept to also include good old regular humans in the same world? Have all of these species evolve at the same time and in the same fashion.

How would the different species interrelate? Since these humans would have grown alongside these other species, would they still be dominant? Or would there be some form of harmony? Maybe a "dog" kingdom or a "cat" kingdom?

You could have a dog PI hunting down a human's cat lover who was kidnapped by a gator.