Mountain glaciers are losing mass rapidly due to anthropogenic climate change. Projections of glacier evolution across the Andes under different warming scenarios have primarily been as part of global scale modelling frameworks, rather than dedicated, regionally optimised, simulations. These global-scale models use simplifications of ice flow physics that may be unsuitable for steep topography, such as that which occurs at mountain valley glaciers. More complex models are available, but with that complexity comes further sources of uncertainty. Here, we assess the sensitivity of the Parallel Ice Sheet Model to ice-flow parameters influencing the ice rheology and subglacial sliding characteristics. We find that the resistance of subglacial material has the most impact on modelled ice outputs (e.g., ice volume), followed by the exponent which relates basal shear stress to sliding, and the threshold velocity at which sliding occurs. The ice-flow rheology enhancement factors, the rate of subglacial water decay, and the maximum water thickness within a presumed subglacial drainage network, can either cause minor variations, or no effect at all, on ice outputs. Our study informs what parameters can potentially be negated in future parameter ensemble tests and provides direction on where further investigation is needed.