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?
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)
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.