It's not advisable at all to allow chins with other animals, as said they can be unpredictable. Even if the cat like Llittlebllonde mentioned is afraid of the chin that can cause them to lash out at the chin one day. Also even if the animal isn't doing anything if the animal goes outside it can bring things in on/in it's fur and/or feet that are toxic to the chin. Also just like rabbits dogs and cats can carry pasteurella, along with other bacteria in it's mouth, so any interaction that the chin comes into contact with the saliva (from a lick, chewing on fur that has been licked, etc) or other bodily fluids (like snot from a dog's nose) can be dangerous. Unless you plan to fully bath the cats and dog before any physical interactions and have them somehow under 100% control at all times and preventing any licking of any kind it's just an accident waiting to happen. Chins are also fairly delicate, they have thin bones (about the thickness of a toothpick) that can break with little pressure so even a playful tap from a cat or even a small dog can be very harmful.
It's up to you, as it's your chin, if you want to take the very risky chance with the chin, but I don't see it worth the risk. I allow my cats and 2 of my 3 dogs (one wants to eat them) in the same room, when I'm in here and with the chins in their cage, but not when they are out of the cage and the room door is closed when I am not in here.