A client of ours is looking for versions of documents that are no longer displayed in the Version History of that document. Is there a way to show more of the existing version history? I did change the number of major versions to a greater number (100) but only ~38 are being displayed.
You need to change the setting for how many versions to keep BEFORE the versions are created. That's the whole point of that setting. If it is set to keep only the last ten versions, say, and a document is saved a hundred times, only the last ten versions will be kept and all other versions will be removed from the system.
When you then change the setting to keep the last 100 versions, SharePoint can't magically recreate the other 90 versions, because they were never kept and are no longer in the system.