How do the feedbacks between tectonics, sediment transport and climate work to shape the topographic evolution of the Earth? This question has been widely addressed via numerical models constrained with thermochronological and geomorphological data at scales ranging from local to orogenic. Here we present a novel numerical model that aims at reproducing the interaction between these processes at the continental scale. For this purpose, we combine in a single computer program: 1) a thin-sheet viscous model of continental deformation; 2) a stream-power surface-transport approach; 3) flexural isostasy allowing for the formation of large sedimentary foreland basins; and 4) an orographic precipitation model that reproduces basic climatic effects such as continentality and rain shadow. We quantify the feedbacks between these processes in a synthetic scenario inspired by the India-Asia collision and the growth of the Tibetan Plateau. We identify a feedback between erosion and crustal thickening leading locally to a <50% increase in deformation rates in places where orographic precipitation is concentrated. This climatically-enhanced deformation takes place preferentially at the upwind flank of the growing plateau, specially at the corners of the indenter (syntaxes). We hypothesize that this may provide clues for better understanding the mechanisms underlying the intriguing tectonic aneurisms documented in the Himalayas. At the continental scale, however, the overall distribution of topographic basins and ranges seems insensitive to climatic factors, despite these do have important, sometimes counterintuitive effects on the amount of sediments trapped within the continent. The dry climatic conditions that naturally develop in the interior of the continent, for example, trigger large intra-continental sediment trapping at basins similar to the Tarim Basin because they determine its endorheic/exorheic drainage. These complex climatic-drainage-tectonic interactions make the development of steady-state topography at the continental scale unlikely.