Back when United was having their 50-states special over a decade ago (awards based on how many states you covered during the time period), I talke to a fellow who flew Minneapolis to San Francisco in seven segments! And the fare was still the basic MSP-SFO fare. He changed planes in something like O'Hare, Omaha, Denver, Salt Lake, Reno, and I forget where else.

At the time, he indicated that if there's a valid connection between two cities, it could be substituted for the non-stop. Such as DEN-SLC-SFO instead of DEN-SFO. Then you break the SLC-SFO into SLC-RNO-SFO. Keep going and you can make a cross-country flight take 10 or more segments (and several days!). Don't know if this is all still true, but it's a start.