The way individual faults and rift segments link up is a fundamental aspect of lithosphere extension and continental break-up. Little is known however about the factors that control the selection of the different modes of rift interaction observed in nature. Here we use state-of-the-art large deformation 3D numerical models to examine the controls on the style and geometry of rift linkage between rift segments during extension of crustal brittle-ductile coupled systems. We focus on the effect of viscosity of the lower layer, the offset between the rift basins and the amount of strain weakening on the efficiency of rift linkage and rift propagation and the style of extension. The models predict three main modes of rift interaction: 1) oblique to transform linking graben systems for small to moderate rift offset and low lower layer viscosity, 2) propagating but non linking and overlapping primary grabens for larger offset and intermediate lower layer viscosity, and 3) formation of multiple graben systems with inefficient rift propagation for high lower layer viscosity. The transition between the linking (Mode 1) and non-linking mode (Mode 2) is controlled by the trade-off between the rift offset, the strength of brittle-ductile coupling, and the amount of strain weakening. The mode transition from overlapping non-connecting rift segments (Mode 2) to distributed deformation (Mode 3) is mainly controlled by the viscosity of the lower layer and can be understood from minimum energy dissipation analysis arguments.