What about this?

1. LOCK the Document in question.  Only the User who locked a Document can unlock it.

2. Create a folder that only the people who are allowed to UPDATE the Document can see - this way only the Document editors can collaborate on the new version.  Load the new version (either an identical copy of the original, or the first approved change) to that folder.

Note that the new folder won't be visible to those who should not see it, and the original Document will now show a lock icon to let everyone know that changes are in process:

Repeat the next 3 steps as many times as needed.

3. Ask for the new Document to be reviewed.  It will be Tagged accordingly and an Activity will be created automatically.

4. Discuss the changes without your file editing program (Office 365 or Google Docs both support this) or do it via the Odoo Chatter Window.  

5. Outside Odoo, merge changes from multiple users (Office 365 and Google Docs both support this).  Then inside Odoo, replace the previous version of the Document with the Document containing the Approved edits.

Once you have repeated 3,4 and 5 enough times to get consencus on the new version:

6. Replace the original version with the final updated version:

6. Unlock the Document.

You can use any Name you want, so you can append a version or just keep the Document the same name even if you change the contents.

Note:  If you would rather keep each version of the document, you can ARCHIVE each version as you go:

You can find all the archived versions (kept in the same folder) with the Search Filter: