  In situ interfacial rheology and numerical simulations are used to
investigate microgel monolayers in a wide range of packing fractions,
$\zeta_{2D}$. The heterogeneous particle compressibility determines two flow
regimes characterized by distinct master curves. To mimic the microgel
architecture and reproduce experiments, an interaction potential combining a
soft shoulder with the Hertzian model is introduced. In contrast to bulk
conditions, the elastic moduli vary non-monotonically with $\zeta_{2D}$ at the
interface, confirming long-sought predictions of reentrant behavior for
Hertzian-like systems.
