I don't think a multi-party system is quite the right goal to aim for. In the current system in the US, people with preferences underserved by both D and R don't just lack a respected party, they face a giant barrier to even making the lack visible. Green-leaning? Fuck 'em, what'll they do -- vote Republican? To make your preference unambiguous by an actual vote, under our system, you have to be seriously into the fringe. This creates a kind of activation-energy barrier to coordinating on a change: very many people can feel that, say, smoking pot is OK, without their preference mattering -- without it even affecting their vote. This fraction could even exceed 50%, unless it's common knowledge that it's over 50%: you don't "throw away" your vote when you expect everyone else to also vote strategically according to preferences which aren't common knowledge.

So a voting system with less of a strategy problem could make common knowledge of real voter preferences easier to arrive at -- the preferences people would honestly vote by, given the chance. You could still have just two major parties, but disciplined by a real option of serious competition if they don't address these no-longer-deniable preferences.

Caveats: 1. AFAIK we still need a clearer understanding of how much strategy people exercise in approval or score voting in practice, once they've gotten used to the new system. And 2. these are just my thoughts as a random citizen trying to see to a way to less large-scale insanity. I'm not a political scientist and I haven't seen one say anything like this about common knowledge and voting systems.

> Many countries which do not use FPTP nonetheless end up with stable long-lived de facto two-party systems

No, they don't. Heck, even many systems that do use FPTP (e.g., the UK) support more parties with representation in the main national legislative body than the US.

A two-party system isn't one where merely there are two stronger parties that tend to form governments or executive administrations.

So as long as there are some seats going to other parties, you don't care if there's an uninterrupted streak of two dominant major parties such that one of them always forms and leads the government?

Because that is the case in many countries, even countries which don't do FPTP, even countries which do things that people argue are good electorally, and that does not seem like a categorical improvement over what happens in, say, the US.

> Because that is the case in many countries, even countries which don't do FPTP,

No, it's emphatically not, especially if you mean exclusively forms the government (not in a coalition.) And, if you don't mean that, it's pretty substantially weaker than the duopoly in the US.

Heck, even FPTP systems that aren't also Presidential systems (another structural factor that reduces competitive parties) generally don't do what you describe, at least in the form of exclusively non-coalition governments.

> and that does not seem like a categorical improvement over what happens in, say, the US.

Whether the difference is merely a substantial quantitative improvement with some creatively-defined common category or a categorical improvement is ultimately immaterial.

Having a third party candidate be a real possibility in a non-FPTP voting system would ensure that there was an escape valve if a party moved too far from the center, right? So it would be strongly motivated not to?