Some recent experiences:
Original flight on UA + *A (not codeshared with a UA flight number): First agent said no same day change on INTL. Called back, second agent said yes at first, but when the agent tried to actually make the change it said I had to pay the change fee and was told the non UA segments made this impossible.
Original flight on UA + *A (codeshared with a UA flight number): First agent said no (because of non UA segment). Second agent said yes and did it.
So I'm guessing there's still some inconsistency and it also depends who you get on the phone.