I don't know how to design a system to encourage such multidimensional parties. A two-party system seems like an inevitable consequence of the fact that there is exactly 1 winner in any election.
Even when a system nominally has more than two parties, there are usually two dominant parties. Other parties either align with one or the other, or are sidelined. People associated with losing parties never seem to be pleased just that their voices were heard.
It's not all or nothing, as the leader of a country doesn't rule alone. Even if a system encourages two dominant parties, the smaller parties can have a big effect. In Canada, the two big (Federal) parties are the Liberals and the Conservatives, and they always win federally.
But it's still not all-or-nothing. For example, the Liberal party often adopts NDP positions if they're gaining popular support. And when the big parties get complacent, they risk losing their "one of two" status. In 2011 in Canada, the NDP was the Official Opposition (second winning party) and the Liberals were a distant third, leading to a big shakeup in strategy. And the provincial parties are different than the Federal parties. I think our system is flawed and too "two party", but the small plurality of parties is what makes Canada a lot less prone to political extremism in my opinion.
Canaidan-Australian Youtuber Paige Saunders has a video arguing that instant runoff voting tempered more extreme politicians in Alaska:
It's my belief that it's Canadians that make Canada a lot less prone to political extremism.
But watch out: America tends to be on the forefront of things. Political extremism persists because it's politically successful. Extremists are enthusiastic, and moderates often follow them because it gets them what they want.
I hope Canadian's cultural adversion to the kind of behavior Americans display will save you for a long time to come. But the fact is that extremism works, and many people will prefer to win against their principles than lose with them.
Political extremism persists because it's politically successful in places where political moderacy isn't. Us Canadians aren't better than Americans, we have a system that allows people to vote more closely to their values and (somewhat) avoid polarization. It's not perfect and a lot of the issues come down to being a "2 Party Lite" instead of a full multi-party democracy.
In my opinion, American Exceptionalism is not a pretension that the USA is the best, but a general assumption that culture primarily drives a nation's systems and not the other way around.
Even when a system nominally has more than two parties, there are usually two dominant parties. Other parties either align with one or the other, or are sidelined. People associated with losing parties never seem to be pleased just that their voices were heard.