How can I remove the 'More' menu item from specific users

I want to remove the "More" menu item from specific users either by Role or Template...can't find anywhere to do that. I need to setup a modified role standard user vs. a message only user to capture fax and vm's. This user will make no calls, and is setup as a modified standard user since I can't control all the proper permissions or apply a template for a message-only user.

I basically want this user completely locked up to only allow the persons who login to this user to be able to download message or faxes via the call log.