We consider classes of T ₆ -orientifolds, where the orientifold projection contains an inversion I _9−p on 9−p coordinates, transverse to a Dp-brane. In absence of fluxes, the massless sector of these models corresponds to diverse forms of N = 4 supergravity, with six bulk vector multiplets coupled to N = 4 Yang-Mills theory on the branes. They all differ in the choice of the duality symmetry corresponding to different embeddings of SU(1,1) × SO(6,6+n) in Sp(24+2n,), the latter being the full group of duality rotations. Hence, these lagrangians are not related by local field redefinitions. When fluxes are turned on one can construct new gaugings of N = 4 supergravity, where the twelve bulk vectors gauge some nilpotent algebra which, in turn, depends on the choice of fluxes.