Some ideas that could have lasted:
A directorial system (like in France between 1795 and 1799): there is not one president, but five directors administrating the country, the secretaries act under their command. Switzerland has a very similar constitution today.
A consular system (France until 1802/04): three consuls with one very powerful first consul lead the government. The executive is very powerful, but electing the consuls and the legislative chambers is a function of the so-called Senate, which is also a constitutional court (the eldest of the world BTW) -> The Senate is a kind of Super-Supreme Court. The sovereignty is vested in the nation.
The Commonwealth of England. Besides the Lord Protector (a president for life), the government consists of a Council of State and the parliament.
A Soviet system. Just let Russia stay in a revolutionary-democratic stage, and you have a model council government.
A direct democracy of the Athenian type, were (almost) all the government agents aren't elected and the legislative power is vested in the people.
Something like a formalized version of the National Convention in France? A unicameral legislature ruling more or less absolutely, with executive authority largely exercised by committees?
Or just enact the 1793 French constitution - a mixture of direct democracy, a mighty moncameral parliament and an elected corporative executive.
Plus you're ignoring all the systems in the world that have supreme power invested in one person, like in North Korea
North Korea officially has a normal, presidential constitution.