Referring to the cat in the box experiment, where the cat either lives or dies based on whether a radioactive atom has decayed or not:
I don't think that two cats exist at once in both the dead and alive state. I don't think that experiences the sickness and death while at the same time the other one experiences normal health. I do believe that when you run a physics *simulation* you will need to keep track or of both possibilities happening at the same time to ultimately get the "right" answer - but I just don't think both possibilities happen.
I've heard teachers say the cat exists in both states until it's observed. I don't buy that. The only thing people have proven is that our mathematical/computational models need to keep track of multiple states to get the answers right. But, because the answers themselves do not involve multiple things at the same time (cats dead and alive), I would argue that nature does *not* necessarily allow the cat to exist in both states at once.
The real question I'm thinking about here is are many versions of everything existing - and I'm guessing no. (Unless somebody can really prove it.)