I'm smoking both turkey and turkey parts this Thankgiving, and I +1 all of the above posts. Separate brines are the way to go.
First, as Dave said, the chemistry changes. I'm no chemist, but as I understand it, brine works by using the process of osmosis to carry flavors and moisture through the meat. At the optimal point of the brine where pressure becomes neutral and the flavors circulate freely, the bird and solution are at equilibrium, meaning there has been change in the solution balance of both the bird, and the brine. So after you started your turkey in the brine, it weakened it, making it less effective on anything else.
Second, you're essentially providing a breeding ground for contaminants. There is plenty of nasty stuff that is slowed in its growth in the fridge, but not stopped. Plus, by taking items out and adding them in, you are increasing the number of opportunities to introduce even more contaminants.
Like they said above...water and salt are cheap.