No general pet food exist, but you could feed some of them the same food.
My ducks, geese chickens and rabbits all eat duck pellets, I just add some additional greens and some meal worms for the chickens. The rabbits occasionally raid my veggie garden, but as they are free range I assume they get what they need from the pellets and their surroundings.
I sometimes give my chickens some wet cat food as well, this is to boost their protein intake in breeding season, I just limit the amount greatly. If I give them eggs for protein, they will eat their own eggs.
My dogs love to steal my cat's pellets, I think they just find it more yummy that their own. My son steals my dog's pellets in return. He just loves it. I am not really concerned with him eating the pellets as the latest food scam test even found kangaroo and snake in our sausages. I do not think a few pellets will do any more harm.