APA actually filed and supported that "Single Carrier" filing, which simply argued that the multiple wholly owned carriers that made up the American Eagle network were homogeneous enough to constitute a Single Carrier for representational purposes. All employees at the time were hired by AMR. All were trained in the same facilities, and usually in combined classes (at least pilots, dispatchers, and FA's). The manuals were all identical. And, all were headed up by ONE Executive management team (of course, each individual division had its own management team, but they were neutered by AMR Eagle Executive level decisions).
AMR made a habit of using the staggered contract negotiations at each carrier to put pressure on whichever carrier might be negotiating a pilot contract at any given time. They'd move airplanes from the carrier in negotiations to one that might have just finished negotiations, resulting in displacements, furloughs, and then offers to the furloughed pilots to come fly the same airplanes at the same bases for the carrier that just got the planes, but as new hires, of course.
It was a total sham.
The NMB ruled that the system was, in fact, a single carrier for representational purposes, which led to the pilots voting in ALPA, rather than APA as the bargaining agent (by then, APA's new leadership had taken on a much tougher stance toward Eagle, and had no interest in representing them, understandably).
Once ALPA was voted in, work to combine all contracts into one began - which would neutralize AMR's ability to whipsaw the groups against each other. The only way AMR would agree to that was the infamous 16 year contract with merely Industry Average yearly pay increases, and periodic arbitrated adjustments about every four years or so - and those adjustments were VERY limited in number and scope. This contract gave AMR steady, dependable, predictable feed costs that they directly controlled, so they were fine with it.
Once that was done, AMR really saw no need to continue with separate divisions, and decided to combine them all and create American Eagle Airlines.
Once the 16 year contract was up, AAG decided that they were going to go with the same model that the other Majors had been using for some time, which was the old multiple carrier whipsaw model. So began the teardown of American Eagle Airlines, brick by brick.
I'm not sure that a Single Carrier petition would be ruled favorably on this time, simply due to the more separate operating nature of the individual carriers this time around. Yes, they are wholly owned, but they are not really combined in any meaningful way, other than through the network name.