Have the legislature be the entire population of the country, direct democracy style. There are a few hours of online parliamentary sessions per day, and votes on all the usual stuff. People are required to either attend, or have a proxy attend. The proxy system would simply mean that you could designate anyone you wanted as your proxy, meaning that they would vote with your vote as well as their own. The proxy would have to choose their own proxy for votes they didn’t attend, and the chains can go to arbitrary lengths. Where they would end are the paid legislators: anyone who commits to actually attend and consider every legislative session, and receive additional briefings and information, could get a job as a legislator. It would pay about the median wage, and would create a large class of people with basically the average interest of their society at heart spending all day considering matters of state. Seems like a good way for the wisdom of the crowds to kick in. Any chain of proxies would be required to terminate on one of these paid legislators.
The executive would be a prime minister figure, in that the election would simply be a normal vote of the legislature, and the President’s tenure could instantly be revoked by the act of that legislature.