Complex patterns of normal faults with multiple orientations and/or highly curved shapes have been traditionally explained by successive tectonic phases of 2-dimensional deformation. Alternatively, multiple fault sets have been proposed to develop simultaneously and in orthorhombic symmetry during a single phase of 3-dimensional deformation. We use analogue models of normal faults to demonstrate that, without the influence of pre-existing structures, 3D extension is preferentially accommodated by the alternate, rather than simultaneous, development of faults with different trends. By means of stress-driven interactions, 3D deformation can be partitioned into coupled systems of normal faults, which display geometries commonly observed in tectonic settings affected by interacting plate boundaries. Under radial extension, deformation is accommodated by major curvilinear grabens coupled with minor perpendicular faults, resulting in the triple junctions of grabens observed in Afar. On the other hand, the alternate development of perpendicular faults accommodates synchronous bi-directional and mutually perpendicular extension, giving the same fault pattern observed in the Barents Sea rift-shear margin.