Can I brine a self-basting turkey?

Short answer, if you trust the brining job of the manufacturer, you won't gain much by rebrining.

In brining you're looking to get a certain amount of moisture "trapped" by the salt in the turkey, which they have, in essence, done for you already with the brining solution. However, that brining solution is usually injected rather than soaked in, so I wonder about the dispersion. Add to that that I actually throw a little sugar into my brining solution (not a lot) and some pickling spice and you can see why you'd want to brine it, but without getting it too salty.

The answer is to go with a longer soak (12 hour or overnight) versus a 4 hour brine, with the lower salt content that you'd use for a long soak. That will balance out the salt levels as the solution's osmotic pressure equalizes. I use 1/2 Cup of table salt per gallon of water. You can leave a turkey in that solution for...a long, long time and it won't be too salty. It's all about equalizing the salt/liquid level inside the turkey.

If you are REALLY concerned about it and have the time, you could soak your turkey in plain water overnight, which would pull out some/most of the brining solution, then brine normally the next day, to put your salt and spices back in. However, I would be concerned about losing some flavor from the turkey that way.

I brined a self basting turkey just last year and I think there was a big (good) difference between that one and other self basting turkeys I have had before. My wife is terrified of food born illness and insists that the thing is cooked way longer than needed and to a higher temp than required. There where two turkeys (same brand bought at the same store and of almost exactly the same size) for the large family gathering cooked on the same day for the same time at the same temperature. Everybody agreed that the brined one was better.

I look at like this. If I where to brine for a few hours, take it out then brine it for another 4 hours what harm could I do?

Like Doug said just go long. I did mine for just over 12 hours using the same brine (the one by Alton Brown) as I always do.

I brine a self basted turkey every year-better flavor, not too salty and very crispy skin. I don't see any reason to pay 2-3 times as much for a fresh or un-basted turkey. You can achieve the same results with the frozen self basted variety. Just be sure to allow enough time to thoroughly defrost your turkey, cut back some on the salt to water ratio, and go with the 'slow' brining method, allowing 8-12 hours for brining. Happy cooking!