  In this article, it is shown that derivator six-functor-formalisms on any
(classical) site canonically extend to higher geometric stacks as defined by
To\"en-Vezzosi under some natural locality conditions. As an application, it is
shown that the six-functor-formalisms of Morel-Voevodsky-Ayoub extend to higher
(Nisnevich-)Artin stacks locally of finite type over some fixed base scheme.
