Among the numerous social structures which you can think of, there are some which seem quite easy to create (essentially associations and companies). However, how are trade unions created? Banks? Insurance companies? Towns? Universities? NGOs?
The one big institutions about which people fantasize are countries: for some reason, people love to create micronations (probably because countries are supposed to be sovereign entities). Yet, that's not the easiest way to start, because it's kind of hard to get recognized as a country, whereas it is probably possible to create most of the other structures (assuming you live in a free country). How come nobody seems to be trying to create this kind of things and report on the result?