The effect of mantle plumes is secondary to that of subducting slabs for modern plate tectonics, e.g. 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 potential dynamics of plume-slab interactions. Substantiating our earlier work which was restricted to 2-D geometries, we observe a range of interesting plume dynamics, including plume-driven subduction terminations, even though the new models allow for more realistic flow. We explore such plume-slab interactions, 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, e.g. 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.