Login to the game with one account. Log out of that account on the web browser (you don't have to keep it open to stay in game). Login to account two on the browser, load up another copy of the game.
Mind you, I've never tried it since I have a second computer to do that on. Logically, as long as your computer can handle two instances of FR running, you should be able to do that. Considering it's a very graphically intense game, it might be a good idea to turn graphics down all the way before attempting this.
Good luck, not completely certain it will work (maybe SOE put in something to block two copies running for all I know!) so hopefully it does for you! :)