If you do want to put your own twist on it and change the solution you can always soak in water to remove some of the initial salt then rebrine for a few hours or can even rebrine just like it is since the salt and liquids will get some osmosis jones action going on and pull the flavorings in.
But wouldn't go more than 6ish hours I'm thinking. Since it's already brined you don't want the meat to begin breaking down.
Otherwise you would be good for up to a 24 hour brine if not injected with any solution.
On the other hand you could always skip any brining/rinsing process and inject that baby with some good "no salt" butter and cajun spices, slowly heat the them then skim the fat that rises to the top. Or you could steam the butter which will help to separate the milk solids from the rest of it
Help for brining a turkey breast
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