“Many different alternative models could fit roughly under the “private city” definition. A foundation called Startup Societies advocates for some of them, such as special economic zones (SEZs), microstates, seasteads, and eco-villages. […] A more explicitly private version comes from Titus Gebel, who runs the website Free Private Cities.”
Scott Beyer wrote about the necessary bottom-up alternatives of Private Cities and others on Catalyst Voices. You can read the full article here: https://catalyst.independent.org/2020/05/20/private-cities-experiment/