2D Manhattan sampling means sampling regularly on a square grid of lines. For such samples, which lie at the union of two rectangular lattices, one dense vertically and the other horizontally, it has been shown that all images bandlimited to the union of the Nyquist regions of the two lattices are reconstructable. In dimension d>=3, there are many extensions of a Manhattan set. This paper characterizes them as unions of rectangular lattices called bi-step, and shows that for any such Manhattan set, all d-dim’l images, bandlimited to the union of the Nyquist regions of its bi-step lattices are reconstructable. Based on a parameterization of bi-step lattices with nice properties and a corresponding partition of d-dim’l frequency space, an onion-peeling reconstruction algorithm is derived.