Have a read of Wengrow and Graeber's The Dawn Of Everything. It's a re-examination of the political implications of archeology, and it's pretty inspiring. Definitely dispelled me of any notion that capitalism or communism or totalitarianism were the only plausible systems.

Ideally, you would find a “philosopher king”, but that’s unlikely to happen. The next best option would be liquid democracy or some sort of direct democracy. If that’s not an option, you could switch to preferential voting that leads to a coalition parliament fairly often. Proportional representation works too. Basically anything other than FPTP.

The Constitution of the Italian Republic and The Constitution Of The Republic of Poland have been interesting to read. Reading about the ways the Knesset and Parliament of the United Kingdom and the Riksdag work has also been interesting. I'm sure the constitution of Germany is interesting too, but it uses a structure that is less similar to the others I've researched recently (elected representatives of the states are involved in choosing federal representatives, whereas in other places local representatives have much less influence on country-wide elections).

It's also interesting to see who is the commander in chief of the armed forces: https://en.wikipedia.org/wiki/Commander-in-chief

In general, I find it hard to design fundamental social institutions (constitutions), but I expect that someone will find a way to improve those that we already have.

In particular, I would not have come up with the Constitution of the Italian Republic if I was working in isolation, but I haven't noticed any major flaws with it (at least for periods of peace: the election of the president requires participation from every region, so if one was occupied by a foreign power such that it could not participate in an election it might be impossible to elect a president). One thought I had is that it might be good to limit the president's ability to dissolve parliament, like limiting that power to cases where the parliament has had a significant amount of time to produce a budget but hasn't actually done so (as is the situation for Poland), to avoid situations where the president says they dissolved the parliament but the parliament says they impeached the president before being dissolved.

Some similarities I've found

Of the states I referred to, there are some interesting similarities I've noticed.

• If there are two legislative bodies, the more populous one has significantly more influence compared to the other.
• The head of government and the head of state are different people. The head of government is a position that probably doesn't have a set term limit and is occupied by someone appointed by the legislature (this is usually called a "Prime Minister"). The head of state is a president or a monarch (and, for a president, there is a set term limit). Often, the consent of the head of state is required in order to appoint a head of government (but this is not true for the Kingdom of Sweden). The head of government actually handles most of the powers of governing, while the head of state provides continuity during the periods when there is no head of government and/or before an elected parliament has convened for the first time.
• The head of state can usually dissolve the legislature (and usually force the removal of the head of government) (but not for the Riksdag of the Kingdom of Sweden, and only in certain circumstances for Poland) in order to have new elections. This might be useful if a legislative body is failing to address critical business due to conflicts between representatives, by allowing voters to elect different people that might actually be able to accomplish more useful things. In comparison, I consider it to be unlikely that any representative or senator in the USA can be removed except by a vote of the legislative body itself: https://politics.stackexchange.com/questions/30455/how-can-a-senator-be-removed-from-office-during-a-term-for-medical-reasons https://discover.hubpages.com/politics/How-Do-I-Remove-a-REpresentative-from-Offfice
• Fundamental obligations and rights are similar. Consider "We call upon all those who will apply this Constitution for the good of the Third Republic to do so paying respect to the inherent dignity of the person, his or her right to freedom, the obligation of solidarity with others, and respect for these principles as the unshakeable foundation of the Republic of Poland." for Poland, and for Italy "The Republic expects that the fundamental duties of political, economic and social solidarity be fulfilled." and "All citizens have equal social dignity and are equal before the law, without distinction of sex, race, language, religion, political opinion, personal and social conditions." and "It is the duty of the Republic to remove those obstacles of an economic or social nature which constrain the freedom and equality of citizens, thereby impeding the full development of the human person and the effective participation of all workers in the political, economic and social organisation of the country.".

Think of a more direct democracy. I will oversimplify enough to annoy those from Switzerland:

Differing levels of law require differing thresholds. Country votes on a law, the majority above the required threshold vote it in. It becomes a national law. That is easy. What about when it fails? Then look to the state level. Did it pass the threshold for your state? Yes? Then it is a state law. Failed state level? Let's look at your county/city/local level. Passed threshold? Local law.

Again, over simplified, but general idea.