  This study explores the link between Modified Gravity and modifications of
phase space volume. Analyzing Fermi gas modifications {in the non-relativistic
limit of the} Ricci-based gravities, we derive a generalized partition function
in the grand-canonical ensemble, connecting Modified Gravity models with the
Generalized Uncertainty Principle. Using this correspondence, we also establish
bounds on the linear Generalized Uncertainty Principle:
$-6\times10^{22}\lesssim\sigma\lesssim 3\times 10^{22}{\text{ s}}/{\text{kg
m}}$, as well as lower bounds for Palatini $f(R)$ gravity $\beta >
-7.51587\times 10^7 \text{ m}^2$ and Eddington-inspired Born-Infeld gravity
$\epsilon > -1.88\times 10^7 \text{ m}^2$, ensuring microscopic stability. This
connection also facilitates testing gravity proposals through tabletop
experiments.
