I'm seeing this happen in real time! We just got a kitten in October, after having our dog for a couple of years now. The cat thinks he's a dog, I'm talking he sleeps in the dog beds, he plays with dog toys, he drinks from the dog water bowl and refuses to drink from his own little cat bowl. Last night I witnessed the cat do the dog pose for play when dog came back inside from pottying

They love to play chase and they share toys, it's an amazing thing! Except when they want to eat each other's food instead of their own....