The operation of a tokamak designed to test the sustainability of a thermonuclear grade plasma like the International Tokamak Experimental Reactor (ITER) presents several challenges. Among them is the necessity of fuelling the plasma to reach the density required to generate enough fusion power to achieve Q = 10 and, at the same time, to protect the divertor from melting by keeping the power density flux impinging directly onto it below 10 MW m−2. Whether this goal is achievable or not depends on the details of the fuelling scheme, of the atomic species that are injected into the plasma, of the power radiation pattern in the scrape-off layer and in the divertor, of the additional heating schemes and of the transport mechanisms at work in the core and near the edge of the plasma. In this paper we present, for different operational scenarios, the results of an integrated modelling approach to the problem taking into account all the different aspects of it. The tool adopted for our simulation is the JINTRAC suite of codes, which can simulate in an integrated fashion the transport of particles and heat in different regions of the plasma. We show that, by carefully tuning the gas fuelling and impurity seeding, it is indeed possible on ITER to achieve Q = 10 and at the same time maintain the divertor in a safe operational condition. We also investigate the sensitivity of this result to the uncertainties in the modelling assumptions underlying the simulations presented in the paper.