The viscosity of suspensions of large (≥ 10 μm) particles diverges at high solid fractions due to proliferation of frictional particle contacts. Reducing friction, to allow or improve flowability, is usually achieved by tuning the composition, either changing particle sizes and shapes or by adding lubricating molecules. We present numerical simulations that demonstrate a complementary approach whereby the viscosity divergence is shifted by driven flow tuning, using superimposed shear oscillations in various configurations to facilitate a primary flow. The oscillations drive the suspension towards an out-of-equilibrium, absorbing state phase transition, where frictional particle contacts that dominate the viscosity are reduced in a self-organizing manner. The method can allow otherwise jammed states to flow; even for unjammed states, it can substantially decrease the energy dissipated per unit strain. This creates a practicable route to flow enhancement across a broad range of suspensions where compositional tuning is undesirable or problematic