Several of Earth's intra-plate volcanic provinces occur within or adjacent to continental lithosphere, with many believed to mark the surface expression of upwelling mantle plumes. Nonetheless, studies of plume-derived magmatism have generally focussed on ocean-island volcanism, where the overlying rigid lithosphere is of uniform thickness. Here, we investigate the interaction between mantle plumes and heterogeneous continental lithosphere using a series of geodynamical models. Our results demonstrate that the spatio-temporal magmatic expression of plumes in these continental settings is complex and strongly depends on the location of plume impingement, differing substantially from that expected beneath oceanic lithosphere. Where plumes ascend beneath thick continental cratons, the overlying lid locally limits decompression melting. However, gradients in lithospheric thickness channel plume material towards regions of thinner lithosphere, activating magmatism away from the plume conduit, sometimes simultaneously at locations more than a thousand kilometres apart. This magmatism regularly concentrates at lithospheric steps, where it may be difficult to distinguish from that arising through edge-driven convection, especially if differentiating geochemical signatures are absent, as implied by some of our results. If plumes impinge in regions of thinner lithosphere, the resulting asthenospheric flow regime can force material downwards at lithospheric steps, shutting off pre-existing edge-related magmatism. In addition, under certain conditions, the interaction between plume material and lithospheric structure can induce internal destabilisation of the plume pancake, driving complex time-dependent magmatic patterns at the surface. Our study highlights the challenges associated with linking continental magmatism to underlying mantle dynamics and motivates an inter-disciplinary approach in future studies.