Yes, DriveHQ supports it.
You need to use our group account service, which is designed for group sharing and collaboration. Group Account service is free and offers 1 free sub-user license. So you can try it for free. Just logon www.drivehq.com, go to My Account, then click on Group Account to become a group account.
Once you become a group account, you can create / add / edit / delete / disable sub-users. You can then create folders in your own account, and you can share different folders to different users (sub-groups, contact groups) with different permissions.
You can also share the same folder again to another user(s) (sub-groups or contact groups) with different permission. When sharing a folder again, please make sure to change the share name as the Share Names must be unique.
Your sub-users can logon and access folders shared to them in the special virtual folder:
They can only see folders shared to them. (Each user also has its own private storage space)
Using DriveHQ FileManager client software, you can directly open a remote file, edit it and save it directly. The file will be saved in a local cache folder first, then automatically sync-ed back to DriveHQ server.