A Microsoft file hosting and synchronization service.
Dear Rory,
Welcome to the forum here.
As you posted in the OneDrive for Business category, about "Can OneDrive do that? ", may I know whether you are using the personal OneDrive online place (www.onedrive.com) or the OneDrive for Business site (https://contoso-my.sharepoint.com/personal/username\_contoso\_onmicrosoft\_com)?
If you are using the OneDrive for Business site, you can just create a folder>share the folder with internal people or external people>the people will go to the shared folder via the shared links in the emails or the direct shared links.
For internal users, they can sync the folder with the OneDrive sync client.
For external users from other companies, you can contact the administrator and let him add the users to your Azure AD and then they can sync the shared folder with the OneDrive sync client as well. If they aren't in Azure AD, they can only upload new files and edit the files in the shared folder.
Best Regards,
Cliff