I think what is not mentioned nearly enough is the need for isolation to prevent decoherence of the cat. You need to make sure the box is it's own universe totally disconnected from the rest. Then I'd say it is a little more intuitive that parallel insides of the box might exist in superposition.
But it also can't be a real cat. Because if it was a real cat then the cat itself collapses the the wave function. Literally any particle interaction does. Really what is important here is that us being on the outside and in a different reference frame (we're assuming we can't do any measurements of things inside the box. Think information barrier) we can't obtain any definite prediction of the cat's state, only probabilistic. The information barrier is the important part here.
