Personally, I'd like to see Mitsubishi get back into the passenger plane business. They're already starting, but with a smaller regional jet.
https://en.wikipedia.org/wiki/Embraer_E-Jet_E2_family#E195-E...
https://en.wikipedia.org/wiki/Airbus_A220#/media/File:CSerie...
I think what's missing in the Airbus-Boeing debate is an appreciation for the role of engine manufacturers. The A220, E195-E2, and Mitsubishi SpaceJet are all built around P&W's new geared turbofan engines.
It seems to me that at this point in the evolution of the industry everybody effectively builds their planes around the capabilities and limits of available engine technology. The immediate cause of death of the A380 was the refusal of any engine manufacturer to design and sell a more modern engine. The A380 became inefficient because its engines were at least 1.5 generations behind, not because there were 4 of them. (Of course, the reason nobody wanted to invest in a newer engine was because the market was too small to make it worth their time, especially considering their struggles with existing commitments.)
I imagine any aerospace engineering company could design a state-of-the-art and competitive body around the available engines. Aircraft manufacturers seem to self-select into market niches not because of engineering costs and difficulties, but simply because the global markets aren't large enough to support a third wide body manufacturer and only barely large enough, if at all, to support another 737/A320.
Embraer's commercial business is owned by Boeing now — the subsidiary is called BBC.
I like thinking about this in a sort of hypothetical Sparta. Sparta had two kings from two different royal lines.
Suppose you're one of two kings, and the other royal line experiences some sort of dynastic hiccup. This inevitably happens to everyone.
A popular strategy throughout history is to capitalize on that hiccup by exterminating the existing royal line, or at least driving them out of power so you can take it yourself. As a king, you are ideally positioned to do this. Maybe you can take both thrones and be the double-king. Maybe you can put your cousin on the second throne. Maybe you can put a flunky on the second throne. Maybe you can get rid of the second throne, leaving yourself as sole king.
But once you do that, a precedent has been set. Your line will eventually stumble too, and it is likely to suffer whatever fate befell the other line the first time. Another strategy you have, back when the rival line first shows weakness, is to stake everything you have on your commitment to upholding the Spartan way of life as expressed in the dual kingship. Give rousing speeches on how unthinkable it would be for anything about the current setup to change. Throw all your considerable resources into supporting the king on the other throne, no matter how weak his position might look.
If that sticks, the other line is likely to remember that you were there when they needed you. But even more than that, you've just established that the dual kingship, and the two families who fill it, are an integral part of the culture, never to be questioned. That tradition may ultimately prove more helpful to you than any personal support. And it has such obvious benefits to the other royal line that, going forward, they will likely support it just as strongly as you do.
On this analogy, the problem with disturbing the Airbus / Boeing duopoly isn't that Boeing might start to compete with Airbus, provoking an arms race. The bigger problem is that (as you mention) some other company might start thinking they can make airplanes too, and who knows what could happen then.