We can't say Compatible or Certified-Compatible until after a new Operating System has been released. And tested. And a Database update released.
So we are going with Copasetic.
This Solution describes compatibility of Big Business 11 and macOS Mojave. (6814)
For Big Business Server 11.14 running on macOS 10.14 Mojave we notice one display issue, that Tabs on the Server Administration windows do not display the bevel effect correctly. This does not seem to cause any problems.
Fundamentally, Mojave shares file system changes from High Sierra. Big Business 11.14 is Certified for High Sierra and appears to work problem free on Mojave.
Conversely, Big Business 10 is not compatible and should not run on Mojave (or High Sierra) as file system changes may cause issues.
In due course, there will be a Certified for Mojave version.