Unlike my previous posts, this will discuss multiplayer game rules that work with any deck format, whether playing Commander, Modern, or anything else.
Horde
Two or more players are "survivors" attempting to cooperatively defeat a self-playing deck. The classic version uses a large number of zombie tokens along with various other zombie creature cards shuffled into a 100-card deck. The horde's cards are revealed and played until a non-token card is played. These creatures have Haste and must attack each turn if able. The survivors attack and block as a team. The horde wins if it reduces the survivor life pool to zero. The survivors win if the horde has no cards to draw and no creatures in play able to attack. Damage to the horde is represented by milling a card for each point of damage.
Assassin
For three or more players in a twist on free-for-all rules. Each player is assigned a secret assassination target, and the objective is to not only be the last player standing, but to score points for finishing off targets. Defeating an opponent means taking over his or her contract, and gaining more opportunities for points.
Two headed Giant
A 4-player variant with two players sharing a turn and a life pool, but playing their own individual decks, on each side. The shared life pool is typically 150% of the usual individual life pool for the deck format.
Star
Also known as Pentagram, Five-Point, and various other names, this game requires 5 players who each have a different mono-color deck. They are seated in order of the color wheel, and each are allied with the two players adjacent while playing against the two players opposite.
Emperor
A six-player format with two teams of three players, where the center player in each team is the "emperor" and the other two to either side are his "generals." The goal is to eliminate the opposing emperor. There is typically a "range of influence" (ROI) rule dictating which opposing players can be targeted by the generals and emperors, either ROI-1 or ROI-2, which affects how much danger the emperor faces and how much danger he presents. Players may tap creatures and transfer them to the control of other allied players.
There are many other variants beyond these, so I encourage any players to find out what is popular in the local game scene and experiment with any new ideas people address. Remember, the core sanctioned rules are just the starting point, and the community of gamers is endlessly inventive.