The best fitting potential 3rd faction I could see is the Scourge under Bolvar. Reformed and united, and open to representing all races.
They have deep history with the Alliance and Horde, but have their own motivations. They have world and political presence. They are neither good nor evil under Bolvar's reign, and now they have room to start a new chapter post Helm of Domination, giving all Scourge room to regain independence.
But it's all too little too late. Faction wars are boring for the specific reason that Factions can not fall, ever. They have plot armor. There is no losing because players are tied to factions. This is why it's pointless to add another faction when the game has shown Alliance can't do shit when Horde loses two Warchiefs and threats to 'end their faction' go empty.