I am an "Editor" (and have also tried this as "Co-Owner") as an external user on a share from a vendor.  I am not able to make any changes to the share.  (For example, the "New +" button is greyed out with the message "You do not have permission to upload or create items in this folder.")  I am on a Mac and have tried this within the Box application/Finder, in Safari, and in Chrome.