To explore the conditions that lead to mountain-building in the case of an oceanic subduction, we conduct analog experiments (with silicon putty upper and lower plates, glucose syrup upper mantle) where subduction is driven by slab pull but also by an underlying mantle flow. Here, plate displacement is not imposed as in most models, but is controlled by the overall balance of forces in the system. We simulate three scenarios: no mantle flow (slab-pull driven subduction), mantle flow directed toward the subducting plate, and mantle flow directed toward the overriding plate. In the case of this latter scenario, we also test the influence of pre-existing rheological contrasts in the upper plate to best reproduce natural cases where inheritance is common. Our experiments show that when plate convergence is also driven by a background mantle flow, the continental plate deforms with significant trench-orthogonal shortening (up to 30% after 60 Myr), generally associated with thickening. We further identify that upper plate shortening and thickening is best promoted when the mantle flow is directed toward the fixed overriding continental plate. The strength of the upper plate is also a key factor controlling the amount and rates of accommodated shortening. Deformation rates increase linearly with decreasing bulk strength of the upper plate, and deformation is mostly localized where viscosity and strength are lower. When compared to the particular natural case of the Andes, our experiments provide key insights into the geodynamic conditions that lead to the building of this Cordilleran orogen since the Late Cretaceous - Early Cenozoic.