On Seasoned Advice, there is a question regarding brining kosher birds. Is there any halachic reason that one cannot brine meat that has already been kashered?
Yes, you can brine koshered meat. That is what corned beef is.
However, it is not quite correct to say,
Once it's been salted & soaked, you can do whatever you want with it. (Corned beef is usually salted & soaked, then pickled, if I'm not mistaken.) – Shalom
It is not permitted to eat it uncooked. It is wasteful to throw it away.
As long as the original salt/blood mixture is washed off (which is required of the Koshering agency), you can re-salt without the kashering requirements. (Shulchan Aruch Y.D. 69:20)
Here in Borough Park, in a Satmar butcher shop, they are selling pickled chicken, and friends of mine where I eat shabbbos have said that they'd had pickled turkey. I'm pretty sure pickled means brined.