  We show that any translate of a model set is a model set in some modified
cut-and-project scheme. Restricting to Euclidean direct space, we show that any
translate of an inter model set is a model set in some modified cut-and-project
scheme with second countable internal space. In both cases, the window in the
modified cut-and-project scheme inherits the topological and measure-theoretic
properties of the original window. Our results hold in fact for a class beyond
inter model sets, which we call almost model sets.
