Extra Modes are configured with extra varieties to the game. They were first introduced on v1.3.5 (aka, The Intense Update), but removed on v2.0.0 and then returned on v2.1.1. There are currently 3 modes. Each mode has separated servers by its own. They can be accessed via the menu or the elevator in the lobby. They're locked and to unlock and access them, you need to get 25 wins.
Available Extra Modes
Big ServerThis mode extends the max player per server to 25 players (back then to 24 players). It was previously named as 20 Player Server. According to that name, it extended to 20 players per server instead.
Super IntenseThis mode locks the Intensity to 5.0 and can't be raised or lowered via the Shop.
ClassicAdded on v1.3.7 and returned on v3.0.0. This mode locks the Intensity to 3.0, can't be raised or lowered via the Shop and restricts Event Icons from spawning. You can still spawn them via the Shop though.
Retired Extra Modes
Some of the modes didn't return after the removal of them.
Hardcore OnlyThis mode forces you to equip a Hardcore Mode Perk to join the round, otherwise you stay in the lobby. To access it, get 10 (Hardcore) wins with Hardcore Mode Perk equipped.
Beginner ModeThis mode locks the Intensity to 1.0 and can't be raised or lowered via the Shop. Players who have passed 50 wins can no longer play it.