The evolution with carrier concentration of the electrical properties of amorphous indium oxide (InOx) thin films has been studied using electric double-layer transistor configurations. Carrier variations of up to 7×1014carriers/cm2 were achieved using an ionic liquid as a gate dielectric. The superconductor-insulator transition was traversed, and the magnitude and position of the large magnetoresistance peak found in the insulating regime were modified. The systematic variation of the magnetoresistance peak with charge concentration was found to be qualitatively consistent with a simulation based on a model involving granularity.