There already are federated social networks. Wikipedia has a long list.[1] You never heard of any of them. Buddycloud, Diaspora and Friendica got far enough to have a number of servers in two digits. Buddycloud seems to have pivoted into a system for in-house use. Diaspora seems to be dying. Frendica is running, with a very modest number of users, and trying to replace itself with a new system called Red.

It's quite possible to do this, but so far, nobody has been able to get anything like enough users to make it useful.

[1] https://en.wikipedia.org/wiki/Comparison_of_software_and_pro...