Inkopolis Tower is where the player accesses the different multiplayer modes, Regular Battle and Ranked Battle. All multiplayer modes are judged by Judd. Inkopolis Plaza can be found outside the tower.
Regular Battle is basically has only one mode, Turf War. It's the simplest game mode focusing on just how much ink is on the ground. Points are earned in relation to how much area covered by the player plus how many kills the player got with kills being worth much less than covering ground. Winning earns the player 300 points in addition to the ones they earned from covering the ground.
Ranked Battle is a more rigorous mode that only unlocks after level 10 is reached. There are three currently known modes of Ranked Battle at this point in time: Splat Zones, Tower Control, and Rainmaker. Splat Zones is a 4-on-4 battle in which the two teams battle for control of a specific area. Tower Control is a mode where two teams battle for control of a tower. If a player is on the tower, it will begin moving towards enemy territory. The team that can get the tower to the other team's base first is the winner. Finally, Rainmaker is a mode that nothing is currently known about.