What kinds of governance designs could exist that aren't common today?
There are at least three democratic designs more successful than our own: Switzerland, China, and Singapore–though TINA shields us from their baneful influence.
If we measure their implementation of six components of democracy:
formal,
elective,
popular,
procedural,
operational and
substantive
we find none follows our Athenian model. Instead, each implements “of the people, by the people, for the people” uniquely.
The first place Swiss invest unimaginable time and energy voting for almost everything: call it 'input legitimacy'. A 37-year-old Zuricher has had the opportunity to take part in 548 referenda, 181 of them federal, 176 cantonal, and 191 municipal. Average turnout is 45% so he has voted in about 246 referenda.
Second place goes to China, both in its citizens' estimation and according to decades of surveys by Gallup, Harvard, YouGov, and Edelman. The PRC’s heavy opinion polling guides policy formation, and amateur politicians provide democratic oversight. It's 90% cheaper than Swiss democracy but still runs it a close second.
Singapore's third-place model blends Confucian officialdom and British parliamentarianism and depends upon outcome legitimacy: the ruling/founding party has always been in power because it so consistently produces good outcomes that nobody seriously considers chancing alternatives.
More on this from Daniel Bell's The China Model: Political Meritocracy and the Limits of Democracy and China's New Confucianism: Politics and Everyday Life in a Changing Society.
For a more comprehensive explanation of China's success read Why China Leads the World: Talent at the Top, Data in the Middle, Democracy at the Bottom, by me.