Task Settings: CEO, Admin tasks private, all other users tasks public

Task Settings: CEO, Admin tasks private, all other users tasks public

Im trying to find a way that our senior management and admins can keep their tasks hidden from everyone (unless they decide to assign to another user in the future). 

These tasks will be associated with accounts, contacts, etc.  Everyone in the company creates and shares all other information (leads, contacts, etc.), so a global setting to keep data private on the senior management Roles will not be a solution.

Thanks in advance for your help.