The effect of mantle plumes is secondary to that of subducting slabs for modern plate tectonics when considering plate driving forces. However, the impact of plumes on tectonics and planetary surface evolution may nonetheless have been significant. We use numerical mantle convection models in a 3‐D spherical chunk geometry with damage rheology to study some of the dynamics of plume‐slab interactions. Substantiating our earlier 2‐D results, we observe a range of interaction scenarios, and that the plume‐driven subduction terminations we had identified earlier persist in more realistic convective flow. We analyze the dynamics of plume affected subduction, including in terms of their geometry, frequency, and the overall effect of plumes on surface dynamics as a function of the fraction of internal to bottom heating. Some versions of such plume‐slab interplay may be relevant for geologic events, for example, for the inferred ∼183 Ma Karoo large igneous province formation and associated slab disruption. More recent examples may include the impingement of the Afar plume underneath Africa leading to disruption of the Hellenic slab, and the current complex structure imaged for the subduction of the Nazca plate under South America. Our results imply that plumes may play a significant role not just in kick‐starting plate tectonics, but also in major modifications of slab‐driven plate motions, including for the present‐day mantle. Plain Language Summary: Subduction of cold, strong lithospheric slabs is the main plate driving force within mantle convection. However, hot upwellings, mantle plumes, may have a greater role in modulating plate motions and slab trajectories than previously thought. We use 3‐D numerical convection models that account for the weakening of rocks due to the accumulation of deformation to understand the effect that mantle plumes can have on subduction zones. We show that plumes can terminate subduction in a range of circumstances. We also test the effect of the amount of internal heating compared to heat from the core which is the major convective control on the importance of plumes. We discuss cases where these plume‐slab terminations may have occurred on Earth, in the geological past, and for the present day through plate reconstructions and consideration of seismic tomography. Key Points: Mantle plumes can terminate subduction in 3‐D, damage rheology convectionPlumes can modulate subducting slabs and plate tectonic regimesPlume‐slab interactions are plausible contributions to the Karoo‐Gondwana event [ABSTRACT FROM AUTHOR]