That is the classic back-to-back scenario and the one I have used occasionally. It is also the one that is disallowed. Someone on FT will provide a sample of the rules, I'm sure, but in brief - they say you cannot intentionally start a second trip before completing the first if the destinations are the same. Of course, there is no problem with booking a new trip after you have begun one because then you would not get the benefit of the advance purchase, etc. And, of course, separate itineraries to other cities don't really sound any alarms, I believe.

By the way, in the new rules announced last month, one of the things UA said they would crack down on was back-to-backs booked by travel agents. The one I use for certain trips actually looks at your record to make sure you aren't doing that and will not make the reservation if so.