We propose a mechanism that explains in one unified framework the presence of continental break-up features such as failed rift arms and high-velocity and high-density bodies that occur along the South Atlantic rifted continental margins. We used 2D and 3D numerical models to investigate the impact of thermo-rheological structure of the continental lithosphere and initial plume position on continental rifting and break-up processes. 2D experiments show that break-up can be 1) “central”, mantle plume-induced and directly located above the centre of the mantle anomaly, 2) “shifted”, mantle plume-induced and 50 to 200 km shifted from the initial plume location or 3) “distant”, self-induced due to convection and/or slab-subduction/delamination and 300 to 800 km off-set from the original plume location. With a 3D, perfectly symmetrical and laterally homogeneous setup, the location of continental break-up can be shifted hundreds of kilometres from the initial position of the mantle anomaly. We demonstrate that in case of shifted or distant continental break-up with respect to the original plume location, multiple features can be explained. Its deep-seated source can remain below the continent at one or both sides of the newly-formed ocean. This mantle material, glued underneath the margins at lower crustal levels, resembles the geometry and location of high velocity/high density bodies observed along the South Atlantic conjugate margins. Impingement of vertically up-welled plume material on the base of the lithosphere results in pre-break-up topography variations that are located just above this initial anomaly impingement. This can be interpreted as aborted rift features that are also observed along the rifted margins. When extension continues after continental break-up, high strain rates can relocalize. This relocation has been so far attributed to rift jumps. Most importantly, this study shows that there is not one, single rift mode for plume-induced crustal break-up.