No, this is not possible, we're afraid. DEVONthink does not allow more than one person to access a database at a time.
DEVONthink follows a decentralized data model where each machine has a local copy of the database but syncs to a commonly accessible location. Collaboration via syncing may require special attention, like a shared account on a cloud service, ie. using the same credentials on each machine. Feel free to contact our support team for further information.
With DEVONthink Server, there is also a built-in web server that allows you to broadcast a database on your network. Users can access shared databases through a web browser, even on Windows machines. While it's not as functional as DEVONthink itself, it can prove useful in an office setting. For more specific information, please refer to the built-in help or manual.