A wide variety of ITER plasmas are investigated using a recently-developed integrated modelling framework, with particular emphasis on the transport and effects of tungsten (W) motivated by ITER's new full-W walls. This workflow is entirely based on theoretical transport models and it has been recently validated against experimental data. Simulations in L-mode and H-mode are performed at different plasma currents and heating powers to assess the maximum W concentrations that allow access and sustainment of H-mode operation, as well as dynamical simulations of the ramp-up, from the limiter to the diverted phase, finding maximum tolerable W concentrations to avoid a radiative collapse of the plasma. A simple physical parameter is shown to order the ratio of W neoclassical to turbulent transport magnitudes for all considered ITER plasmas as well as previously simulated ASDEX Upgrade experiments.