We present three-dimensional deep-mantle laboratory models of a compositional plume within the vicinity of a buoyancy-driven subducting plate with a fixed trailing edge. We modelled front plumes (in the mantle wedge), rear plumes (beneath the subducting plate) and side plumes with slab/plume systems of buoyancy flux ratio spanning a range from 2 to 100 that overlaps the ratios in nature of 0.2–100. This study shows that 1) rising side and front plumes can be dragged over thousands of kilometres into the mantle wedge, 2) flattening of rear plumes in the trench-normal direction can be initiated 700 km away from the trench, and a plume material layer of lesser density and viscosity can ultimately almost entirely underlay a retreating slab after slab/plume impact, 3) while side and rear plumes are not tilted until they reach ∼600 km depth, front plumes can be tilted at increasing depths as their plume buoyancy is lessened, and rise at a slower rate when subjected to a slab-induced downwelling, 4) rear plumes whose buoyancy flux is close to that of a slab, can retard subduction until the slab is 600 km long, and 5) slab–plume interaction can lead to a diversity of spatial plume material distributions into the mantle wedge. We discuss natural slab/plume systems of the Cascadia/Bowie–Cobb, and Nazca/San Felix–Juan Fernandez systems on the basis of our experiments and each geodynamic context and assess the influence of slab downwelling at depths for the starting plumes of Java, Coral Sea and East Solomon. Overall, this study shows how slab/plume interactions can result in a variety of geological, geophysical and geochemical signatures.