Two companies, Boeing and Airbus, have dominated the aviation industry for decades. But Boeing's recent struggles with safety this year, as well as production shortages for both planemakers, could be pushing carriers to wonder whether it's time to change up the competitive landscape.

"We need more competition in the aerospace business," United Airlines CEO Scott Kirby said on the Air Show Podcast, according to aviation outlet The Air Current. Kirby said his airline wasn't ready to splurge on planes from a non-Airbus, non-Boeing manufacturer just yet, but that it has "just started thinking" about cultivating a new supplier.

Boeing is still grappling with fallout from early January, when the door plug of a Boeing 737 Max 9, operated by Alaska Airlines, blew out midflight. That spurred closer scrutiny of Boeing's manufacturing processes. The company has slowed production of its planes, annoying carriers who were expecting to receive Boeing jets this year.

Kirby has complained about Boeing's struggles before, calling the 737 Max 9's temporary grounding in January, ordered by the U.S. Federal Aviation Administration, the "straw that broke the camel's back."

Boeing's competitor Airbus is also facing problems. Parts and labor shortages are reportedly forcing the European planemaker to delay deliveries to carriers. Hundreds of Airbus 320neo jets will also need to be grounded to replace faulty components in engines produced by supplier Pratt & Whitney.

COMAC as a third supplier?

But who might that third supplier be?

One possibility is COMAC and its C919 narrow-body jet, similar to Boeing's 737 and Airbus's A320. The Chinese state-owned manufacturer debuted the C919 at the Singapore Air Show earlier this year in its first international showing.

At the Fortune Innovation Forum earlier this year, Cathay Pacific CEO Ronald Lam suggested that the aviation world could be moving towards an "ABC market": Airbus, Boeing and COMAC. The head of Hong Kong's flagship airline, which currently uses both Boeing and Airbus jets, suggested that such "triangular competition" would be good for the industry.

Kirby, in his comments to the Air Show Podcast, isn't quite so sure. "It's not inevitable, I think it's unlikely," he said, in response to a question about whether a third supplier will be Chinese.

So far, only China-based airlines have committed to purchasing the C919, though Saudi Arabian airlines have reportedly expressed some interest in COMAC's work. The C919 still needs to be approved by the European and U.S. regulators before it can operate commercially in those markets.

Even COMAC’s regional jet, the ARJ21, which has been in commercial use since 2016, has yet to be approved by U.S. regulators. (A small Indonesian airline is the only non-Chinese carrier to use the ARJ21)

Instead, Kirby thinks a new challenger could be Brazil’s Embraer.

Embraer is the industry's third-largest manufacturer behind Boeing and Airbus. The Brazilian company currently manufacturers smaller regional jets with a capacity of just under 100. Yet Embraer is exploring the possibility of creating a next generation narrow-body jet, the Wall Street Journal reported in May.