Is this even possible?

I was wondering if there is a way to Link a specific category to three different sites? For example you have Site1 Site2 Site3, which are basically 3 identical copies of each other on different hosting accounts (Same hosting company). So I have Category1 Category2 and Category3, I want to make Category4 so that if you are on any of the 3 sites and you are an admin you can make a post and put it in Category4 and it will post to all three sites. oh and I would like it to only be accessed and viewable if your logged in as admin ??

Hope i explained myself properly.