Theatrhythm Final Fantasy has two ways of interacting with other players: StreetPass and Chaos Shrine.
Players can make ProfiCards and exchange them via StreetPass. Options for customizing cards become available as you earn Rhythmia. You can also attach Dark Notes to your ProfiCard, as a way of gifting them to other players.
Although this mode is playable solo, it can also be played by up to four people with 3DS's and copies of the game. Only local play is available, not online.