The thick crust of the southern Tibetan and central Andean plateaus includes high-conductivity, low-velocity zones ascribed to partial melt. The melt origin and effect on plateau uplift remain speculative, in particular if plateau uplift happens before continental collision. The East Anatolian Plateau (EAP) has experienced similar, more recent uplift but its structure is largely unknown. Here we present an 80 km deep geophysical model across EAP, constrained by seismic receiver functions integrated with interpretation of gravity data and seismic tomographic, magnetotelluric, geothermal, and geochemical models. The results indicate a 20 km thick lower crustal layer and a 10 km thick mid-crustal layer, which both contain pockets of partial melt. We explain plateau uplift by isostatic equilibration following magmatism associated with roll-back and break-off of the Neo-Tethys slab. Our results suggest that crustal thickening by felsic melt and mafic underplate are important for plateau uplift in the EAP, Andes and Tibet.