Friction force microscopy (FFM) explores the interaction in a sliding contact on the nanoscale, providing information on the frictional dynamics and lateral contact stiffness with lattice resolution. Recent FFM measurements on a NaCl crystal immersed in liquid (ethanol) surroundings displayed an increase of the effective contact stiffness, K_eff, with the applied load, differently from similar measurements performed under ultra-high vacuum (UHV) conditions, where K_eff showed negligible load dependency. Additionally, under UHV conditions multiple slip length friction with increasing load was reported, while in ethanol surroundings only single (lattice unit length) slips were observed. Our current understanding of this behavior relates the transition from single jumps to multiple jumps dynamics to the normal load (manifested through the amplitude of the interaction potential at the contact, U₀) and to the damping of the system. Here we have incorporated the effect of the load dependency on both U₀ and K_eff within Prandtl‒Tomlinson based simulations, accompanied by variations in the damping coefficient of the system. Introducing the experimentally observed load dependency to K_eff resulted indeed in single slip jumps at critical damping, while multiple slip jumps were obtained at constant K_eff. The average slip length increased with the normal load, particularly when the system became underdamped. Our work provides a glimpse on the relation between the characteristic observables in atomic-scale sliding friction (maximal slip forces, stiffness, and slip dynamics) with respect to their governing parameters (corrugation energy, effective stiffness, and damping). While common understanding in nanotribology relates the effect of surrounding media mainly to the interaction potential at the contact, here we show that the media can also greatly affect the elastic interaction, and consequently play an important role on the transition from single to multiple stick-slip.