No, at least not yet. There is only one single "Company Folder" automatically shared with all users and you cannot fine-tune the access.
Yes, sadly this is a feature that hasn't yet been rolled out... Being able to share folders would be awesome.
For that single Company folder, we use a naming convention to group workspaces within it. For example, all our template names begin with "ConsBI-". Or you could label reports for the SEO team beginning with "seo-". This provides an easy handle to search on or you can then sort the name column alphabetically to group reports.