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A solution is obtained for the high-frequency scattering by a pair of parallel wedges where the edge of one wedge is illuminated by the shadow boundary field of the other. A generalized spectral extension of the uniform GTD is used to determine the contribution from the doubly diffracted ray. Expressions for the diffracted field are given for plane, cylindrical, and spherical wave illuminations. Incidence oblique to the edges is also considered. These expressions reduce to a closed form at the shadow boundaries and outside the overlapping transition regions where the results coincide with those obtained by the uniform GTD augmented by slope diffraction. The solutions to the scalar problems are then used to derive a dyadic diffraction coefficient for the doubly diffracted field, in the ray-fixed coordinate system. The general expressions presented here directly apply to the diffraction by half planes, strips, and joined wedges (thick edges) where the number of terms involved significantly reduces.