score:5
It almost certainly depends on the ticket, but unless it's a fully flexible ticket, I doubt you can do this cheaply, or possibly at all. The ticket is most likely a ticket from Tokyo to Rio; the airline treats the connection as incidental. In fact, in practice they could even send you a different route (not via LA) if it made sense to do so on the day (weather etc.). In most cases you aren't allowed to break your journey up, therefore, as that would be a different trip.
The only way you'll know for sure is to call the airline and ask, but if your tickets are non-refundable, prepare to spend a lot of money to make this change.