The tectonic interaction, linkage, and coalescence of propagating continental rift segments eventually create a through-going axial rift floor without which a break-up axis cannot develop. However, prior to linkage, interacting rifts are separated by a topographic basement-high (rift interaction zone, RIZ) which is progressively dismembered and down-thrown by the lateral propagation of rift-tip faulting and their hanging wall subsidence. Here, we explore the evolution of the Middle Shire and Nsanje RIZs located along three contiguous non-volcanic propagating rift segments: the southern Malawi Rift (SMR), Lower Shire Graben (LSG), and the Nsanje Graben (NG), East Africa. The Middle Shire RIZ is an overlapping-oblique divergent RIZ in which the NNE/N-trending SMR is propagating southwards into the shoulder of the NW-trending LSG, whereas the Nsanje RIZ is a tip-to-tip oblique RIZ in which the LSG has propagated southeast into the northern tip of the N-trending NG. We utilize field observations and a landscape evolution model with implemented fault displacement fields of two contiguous RIZs with contrasting geometries, to simulate their geomorphic evolution, and apply a static stress model to evaluate the stress transfer patterns during RIZ evolution. The model results provide insights into the natural observations in the study area, in which, with progressive extension and tip growth, the Middle Shire RIZ maintains minor basement down-throw and an unequilibrated axial stream profile, which contrasts the widespread basement burial and equilibrated axial stream profile across the Nsanje RIZ. Modeled static stress distribution predicts compounding stress concentrations at tip-to-tip RIZs (synthetic border fault interactions), favoring brittle strain localization and rift coalescence, and stress relaxation at overlapping divergent RIZs (antithetic border fault interactions), favoring stalled rift coalescence. We argue that RIZ and rift border fault geometries, and their kinematics strongly influence the pace of rift coalescence by modulating the spatial distribution of tectonic stresses necessary to promote rift-linking deformation.