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.