Will their system actually let you do that in that order? Or will it kick it out seeing you are already booked?
Once we had a Princess cruise booked way in advance for our 30th wedding anniversary. It was in advance of when airline schedules were out for the time period. Our TA advised us to book EZ Air to make sure we had airline reservations, and then when airfares came out, check them out. He said we could always delete the EZ Air before final payment. I found a great airfare special online, but every time I tried it, I got a technical difficulty pop-up. After several unsuccessful attempts, I called the number shown in case you had technical difficulties. The first thing the airline representative said to me after I explained was my wife's name. I had not given this to her. It seems the flight with the special rate I had found was one that Princess had already booked us, and they could not book us as we were already booked. I explained to her that we had only paid a deposit to the cruise line and could cancel the flight reservation until final payment. She advised me to cancel and then do the special internet rate. I told her I did not at any point want to not have a flight, and she finally cancelled and rebooked us at the new rate making me promise to call our TA and let him know we had cancelled the flight through Princess, which of course I did right after hanging up.
The point is computers will kick out a new reservation in the same names as people who already have a reservation.