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We propose a unifying rheological framework for dense suspensions of non-Brownian spheres, predicting the onsets of particle friction and particle inertia as distinct shear thickening mecha- nisms, while capturing quasistatic and soft particle rheology at high volume fractions and shear rates respectively. Discrete element method simulations that take suitable account of hydrody- namic and particle-contact interactions corroborate the model predictions, demonstrating both mechanisms of shear thickening, and showing that they can occur concurrently with carefully selected particle surface properties under certain flow conditions. Microstructural transitions as- sociated with frictional shear thickening are presented. We find very distinctive divergences of both microstructural and dynamic variables with respect to volume fraction in the thickened and non-thickened states.