Based on gamemodes suggested by two people at around the same time.

Best of 5 (Bo5)
5 points are available one at a time, capturing each unlocks the next one for both teams, the first team to capture 3 points wins.

Spawns move up every two points and teams respawn with every cap.

Best of 3 (Bo3)
3 points are available one at a time, capturing each unlocks the next one for both teams, the first team to capture 2 points wins.

Spawns move up every point and teams respawn with every cap.

Thanks to Egan for helping with this.