<p>Once surface active colloids, such as microgels, adsorb to an interface, they modify the viscoelastic properties of the interface. In contrast to what happens in bulk, the elastic properties have a non-monotonic dependence on the generalized area fraction. In this study, we describe this phenomena by performing molecular dynamic simulations of effective pair potentials in two dimensions. Our potential model is constructed by taking available interfacial rheology experimental results as a starting point. From this knowledge, we need to take into account, for very dense monolayers, that the interaction between adsorbed microgels has to consider multiple factors, including an increase in microgel stiffness when compressed and the presence of a dense inner core region. To account for these properties, we adopt a square-shoulder multi-Hertzian model, which predicts equilibrium structures and rheological properties in qualitatively agreement with experiments. Crucially, this model avoids the reentrant liquid behavior commonly observed with soft Hertzian-based pair potentials at high concentrations. Building on these insights, we thus explore the parameter space of this potential, providing novel predictions for dense monolayers composed of differently crosslinked microgels, awaiting for experimental investigation in the near future.</p>