Hi John,
Set up one of your machines in your local network with a fixed IP address to host the database. Install Davinci Resolve Project Server software on this machine PLUS the PostgresSQL database via the DaVinci Resolve software installer.
Launch Resolve Project Server and create a database, then on any other machine connected to the same network as your host computer, you can connect to this database using the PostgreSQL option and the fixed IP address of your host machine. That’s it. Then you can create projects on this database, turn on collaboration in the project and others can open it at the same time.
Do you have mixed machines or all macOS or Windows?