The competition between the impact of inherited weaknesses and plate kinematics determines the location and style of deformation during rifting, yet the relative impacts of these ‘internal’ and ‘external’ factors remain poorly understood, especially in 3D. In this study, we used brittle-viscous analogue models to assess how multiphase rifting, that is changes in plate divergence rate or direction, and the presence and orientation of weaknesses in the competent mantle and crust, influences rift evolution. We find that the combined reactivation of mantle and crustal weaknesses without any kinematic changes already creates complex rift structures. Divergence rates affect the strength of the weak lower crustal layer and hence the degree of mantle-crustal coupling; slow rifting decreases coupling, so that crustal weaknesses can dominate deformation localisation and surface structures, whereas fast rifting increases coupling and deformation related to mantle weaknesses can have a dominant surface expression. Through a change from slow to fast rifting mantle-related deformation can overprint structures that previously formed along (differently oriented) crustal weaknesses. Conversely, a change from fast to slow rifting may shift deformation from mantle-controlled towards crust-controlled. When changing divergence directions, structures from the first rifting phase may control where subsequent deformation occurs, but only when they are sufficiently well developed. We furthermore place our results in a larger framework of brittle-viscous rift modelling results from previous experimental studies, showing the importance of general lithospheric layering, divergence rate, the type of deformation in the mantle, and finally upper crustal structural inheritance. The interaction between these parameters can produce a variety of deformation styles that may, however, lead to comparable end products. Therefore, careful investigation of the distribution of strain localisation, and to an equal extent of basin depocenter locations over time is required to properly determine the evolution of complex rift systems, providing an incentive to revisit various natural examples.