This isn't exactly the same scenario, but in 2011 I had a Y ticket JFK-MXP-JFK. I called to ask about upgrading the outbound flight only. It took the agent a long time to price and it ended up being too expensive so I passed. When I checked online I had two JFK-MXP legs in the itinerary (one in Y and one in J). I called back to have them close out the J leg, but before I could say anything the agent said "Hold on, there's an issue with your itinerary. I need to reissue the ticket before we can proceed". He came back after a few minutes and I then made up a stupid question and when we hung up I got an e-mail with a new ticket # that included the J flight on the outbound.

So if you have 2 overlapping flights the ticket hasn't been reissued and you'll need to call to get it sorted out. But maybe when you call back you'll get lucky like I did...