  This paper introduces an endofunctor $\VT$ on the category of frames,
parametrized by an endofunctor $\T$ on the category $\Set$ that satisfies
certain constraints. This generalizes Johnstone's construction of the Vietoris
powerlocale, in the sense that his construction is obtained by taking for $\T$
the finite covariant power set functor. Our construction of the
$\T$-powerlocale $\VT \bbL$ out of a frame $\bbL$ is based on ideas from
coalgebraic logic and makes explicit the connection between the Vietoris
construction and Moss's coalgebraic cover modality.
  We show how to extend certain natural transformations between set functors to
natural transformations between $\T$-powerlocale functors. Finally, we prove
that the operation $\VT$ preserves some properties of frames, such as
regularity, zero-dimensionality, and the combination of zero-dimensionality and
compactness.
