Y A typical dense non-Brownian particulate suspension exhibits shear thinning (decreasing viscosity) at low shear rate or stress followed by a Newtonian plateau (constant viscosity) at intermediate shear rate or stress values which transitions to shear thickening (increasing viscosity) beyond a critical shear rate or stress value and finally undergoes a second shear thinning transition at extremely high shear rate or stress values. In this study, we unify and quantitatively reproduce all the disparate rate-dependent regimes and the corresponding transitions for a dense non-Brownian suspension with increasing shear rate or stress. We employ discrete particle dynamics simulations based on the proposed mechanism to elucidate its accuracy. We find that a competition between interparticle interactions of hydrodynamic and nonhydrodynamic origins and the switching in the dominant stress scale with increasing the shear rate or stress lead to each of the above transitions. Inclusion of traditional hydrodynamic interactions, attractive or repulsive Derjaguin-Landau-Verwey-Overbeek (DLVO) interactions the interparticle contact interactions, and a constant friction (or other constraint mechanism) reproduces the initial thinning as well as the shear thickening transition. However, to quantitatively capture the intermediate Newtonian plateau and the second shear thinning, an additional nonhydrodynamic interaction of non-DLVO origin and a decreasing coefficient of friction, respectively, are essential, thus providing an explanation for the presence of the intermediate Newtonian plateau along with reproducing the second shear thinning in a single framework. Expressions utilized for various interactions and friction are determined from experimental measurements and hence result in excellent quantitative agreement between the simulations and previous experiments.