On the separate ticket side, LATAM won't usually even check LATAM to LATAM connections! Had to get a supervisor to override the system heading to EZE through SCL when I had to wait to find out exactly when I could pop over the Andes (EZE on the outbound or the return leg). Only took the MIA gang about 45 minutes to figure things out. Bags ended up on the flight to EZE right before my booked one.

Of course with LAN YMMV