The sims 3 is a pure singleplayer game, multiplayer is not an option. So no playing together.
The next part is speculation, I don't know if it is possible or not.
It might be possible to play sequentially by using the same save. But that would require you to send the save file manually after each session to the next person.
The system would be:
- Player 1 plays a session.
- Player 1 saves his game.
- Player 1 locates his save file and transfers it to player 2.
- Player 2 places the received save in the correct folder.
- Player 2 plays his session and saves.
- Player 2 passes the save to player 3.
- Player 3 receives and places the save correctly.
- Player 3 plays his session and send the save back to player 1.
- Go back to point 1.
This assumes that the players only manipulate their own sims though. And nothing stops a player to change anything an earlier player did.