  Recently, the idea of taking ensemble average over gravity models has been
introduced. Based on this idea, we study the ensemble average over
(effectively) all the gravity models (constructed from Ricci scalar) dubbing
the name \"uber-gravity which is a {\it{fixed point}} in the model space. The
\"uber-gravity has interesting universal properties, independent from the
choice of basis: $i)$ it mimics Einstein-Hilbert gravity for high-curvature
regime, $ii)$ it predicts stronger gravitational force for an
intermediate-curvature regime, $iii)$ surprisingly, for low-curvature regime,
i.e. $R<R_0$ where $R$ is Ricci scalar and $R_0$ is a given scale, the
Lagrangian vanishes automatically and $iiii)$ there is a sharp transition
between low- and intermediate-curvature regimes at $R=R_0$. We show that the
\"uber-gravity response is robust to all values of vacuum energy, $\rho_{vac}$
when there is no other matter. So as a toy model, \"uber-gravity, gives a way
to think about the hierarchy problems e.g. the cosmological constant problem.
Due to the transition at $R=R_0$ there is a chance for \"uber-gravity to bypass
Weinberg's no-go theorem. The cosmology of this model is also promising because
of its non-trivial predictions for small curvature scales in comparison to
$\Lambda$CDM model.
