ymarks browser extension:

Support for your browser is under way. :-)

Please note that these downloads are not as thoroughly tested as you probably would expect them to. Proceed with caution.

ymarks is a free and open source add-on for several modern web browsers with a server component written in C that allows you to synchronize your browser's bookmarks with an SQLite3 database that can be hosted either on your local machine or somewhere in your intranet (or even the internet). It is supposed to be a single-user system in order to reduce complexity and increase privacy, but you can (technically) run as many parallel instances of ymarks as you like.

Alternatives: had an article about potential alternatives if you can't stand ymarks.
A NANY 2018 project.