Any time you introduce a new dog into your "pack", there will be fights over who is the "leader" in the canine area. I have been through this four times with my Alpha Male (it was the cat once. They sleep together now, and the cat rides his back around the yard). I got a new female today, and Colt sniffed her, then "asserted" himself to let her know who was boss. She is Beta, so she readily accepted her position after a few fights. The problem with continual fighting may be that you have two Alphas. When I went searching for a companion for him, I specifically looked for a Beta female (since alot of males won't accept another male AT ALL). The pairing went beautifully. They are lying in the floor sleeping right next to each other as I am typing now. Hope the info on the Alpha/Beta issue sheds some light on the potential problem Good luck!!
Good luck!!