How to coordinate document production better?

In our department, we produce reports written by various people, and coordinated by a country manager for that particular report. The country manager provides original text, tables, and figures for the report, which our editor reviews and edits, and then we "format" the various elements, meaning we clean up the text using Word paragraph styles and so on, according to our style manual, as well as formatting tables and figures (graphs) to make them consistent and compliant with our style manual, and put it all together into a cohesive publication.

The process usually doesn't go very smoothly, however, with several rounds of corrections before and after formatting, and sometimes there's confusion about which chapters (each chapter is its own Word file) have or have not been edited.

Is there a software package that would allow us to better organize our document production workflow? One that might enable us to "check out" files while they're being edited or formatted so that no one else can make changes or copy the files to work on?

We've thought of organizing things in folders, but people can still make "unauthorized" edits to the files, etc.

Any help would be greatly appreciated. Thanks!