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Extensional tectonic settings may undergo time-dependent kinematic changes, causing a multiphase evolution of the resulting fault networks. Yet, the spatial and temporal evolution of fault networks during triaxial and biaxial strain remains underexplored. Here we present scaled analogue models to investigate fault geometry, activity, and patterns across multiple phases of triaxial (constrictional) and biaxial (plane) strain. Our models show that (a) during the shift from biaxial to triaxial strain, first-phase normal faults are fully reactivated and new conjugate sets of oblique-slip faults develop during the subsequent triaxial phase. (b) During the shift from triaxial to biaxial strain, first-phase conjugate sets of oblique-slip faults either become inactive or are partly reactivated, while being cut across and linked up by new faults during subsequent biaxial strain. Our results illustrate kinematic interactions within multiphase fault networks, showing how perturbations in stress domains control the geometry of new faults and how earlier dominant faults create mechanical obstacles that hinder fault propagation. Finally, we compare the fault network evolution in our models to natural examples. The transition from biaxial to triaxial strain reflects the two-phase deformation observed in the Aegean Sea, where pre-existing normal faults were reactivated and new oblique-slip normal faults developed. Similarly, a shift from triaxial to biaxial strain explains the faulting patterns in the Barents Sea during the Late Mesozoic to Early Cenozoic, which exhibit abandoned, reactivated, and newly developed faults.