Phantom Thieves Alliance is an online feature in Persona 5.
The Phantom Thieves Alliance allows players to opt in and can pitch in during battles and dungeon-crawling. A teammate who is knocked out can be taken hostage by an enemy during battle, and if the player fails to save them, someone they're connected to online can step in. They can also prevent enemies from running away on the map so that a player can defeat them and continue on undetected.
As for the player's day-to-day, online functionality takes the form of inspiration for those unsure of how to spend their downtime. What other Phantom Thieves are doing in-between battles is recorded for everyone to check, and questions asked during class now come with a percentage of players who chose each possible answer.