Like how clan war battles for Super Smash Bros Brawl is done.
This will keep the balance of teams in check. It's more of a team game now than ever. Prevents good players from sweeping easily.
Team 1 has Members A C E
Team 2 has Members B D F
Each member has a 2 game loss allowance. For instance, A vs B. A loses Game 1 but wins Game 2 and 3. B is out forever now because he lost 2 games. A is still alive, and is able to play D. When A vs. D, D wins Game 1. A is automatically out now. D is alive and is only eliminated when he loses 2 games, whether it's in the same series or different.
It's just an idea - I'd guess you'd want to save the best for last, and that's not a bad idea. But it really promotes teamwork because if a lesser skilled player even takes one Game off the better opponent, it's still a good shot he'll get knocked off by a teammate in one game.
You can do it like Seasons, where Team 1, 2, 3, 4, 5 have to play their matches in 7 days. You can do lineup order in advance as to prevent mid-week switching of players. You can make sure each Team plays each other once. You can determine winners various ways
I also believe there should be more factions and less players in each one. Split every good player and make them leader of that group.
-5-6 of the Best players deserving of a Faction.
-5-6 teams of 3 or 4 players in total
-Stock Style battle
This promotes the most even playing field for all Factions. Any team can get a chance to win the 'title' for that Season or Time Period. Make this bi-weekly so there is more parity amongst the winners
PS I'm not Factioning