I have one flight with one connection: Tokyo to Rio with a stop in LA.
I'd like to postpone my trip from LA to Rio to stay some days in the US, but I was not able to this at the airline website (United Airlines).
The only thing I was able to do is to change the flight Tokyo-Rio to a Tokyo-LA and add another flight LA-Rio, but this is as expensive as buying new tickets.
My tickets are non-refundable and "change fee", so I thought I couldn't miss this connection but I could previously change the dates.