  Granular media take on great importance in industry and geophysics, posing a
severe challenge to materials science. Their response properties elude known
soft rheological models, even when the yield-stress discontinuity is blurred by
vibro-fluidization. Here we propose a broad rheological scenario where average
stress sums up a frictional contribution, generalizing conventional
$\mu(I)$-rheology, and a kinetic collisional term dominating at fast
fluidization. Our conjecture fairly describes a wide series of experiments in a
vibrofluidized vane setup, whose phenomenology includes velocity weakening,
shear thinning, a discontinuous thinning transition, and gaseous shear
thickening. The employed setup gives access to dynamic fluctuations, which
exhibit a broad range of timescales. In the slow dense regime the frequency of
cage-opening increases with stress and enhances, with respect to
$\mu(I)$-rheology, the decrease of viscosity. Diffusivity is exponential in the
shear stress in both thinning and thickening regimes, with a huge growth near
the transition.
