Yes they do, but their willingness to do this is simply a factor of loads on the respective flights. 2 days ago I was booked DTW-NRT-PVG (744 all the way), and just before boarding the GA in DTW paged me and asked if I'd prefer the nonstop. Those flights (DTW-NRT and DTW-PVG) leave at exactly the same time (3:30pm) and it appeared they were doing some shuffling. I declined because I hate the 777ER BE seats, and I was meeting someone at PVG late that night and preferred to burn time at the NRT club vs. the PVG arrivals hall.

If load reshuffling isn't favorable you don't stand much of a chance of switching - the typical DL response in those situations is something to the tune of "this would have to be reticketed, blah blah..."