The linkage and coalescence of propagating continental rifts create through-going rift floors necessary to localize the breakup axis. Prior to linkage, interacting rift tips are separated by a topographic basement-high (rift interaction zone, RIZ), which is progressively dismembered and down-thrown by the propagation of rift-tip faulting and basin subsidence. Here, we explore the evolution of Middle-Shire and Nsanje RIZs located along three active, contiguous, amagmatic rifts in East Africa. The Middle-Shire RIZ is an overlapping-oblique divergent RIZ across which the southern Malawi Rift is propagating into the Lower Shire Graben (LSG) shoulder, and Nsanje RIZ is a tip-to-tip oblique RIZ across which the LSG has propagated into the Nsanje Graben tip. Utilizing field observations and landscape evolution models of contiguous RIZs with contrasting geometries, our results predict that with progressive extension and tip propagation, the Middle-Shire RIZ maintains minor basement down-throw and unequilibrated axial stream profile, which contrasts pronounced basement burial and equilibrated axial stream profiles across the Nsanje RIZ. Modeled stress distribution predicts compounding stress concentrations at tip-to-tip RIZs via synthetic border fault interactions, favoring rift coalescence, and stress relaxation at overlapping divergent RIZs favoring stalled coalescence, altogether demonstrating that RIZ geometries and kinematics strongly influence the pace of rift-tip coalescence.