Adding Borderlands GOTY to Library While Having the Base Game

Hello, so I own the base game and the General Knoxx DLC. Say I traded for a copy of Borderlands GOTY, will I be able activate it so that I will have the base game and all the DLCs? I think I know the answer but just wanted to make sure. I'm asking because it won't let me buy the game from the Steam Store page straight to my library saying I already own the game.

Also, I already know that I won't be able to give away the base game and the DLCs that I previously had after doing so.