We study multiple electron transfer from a CdSe quantum dot (QD) to ZnO, which is a prerequisite for successful utilization of multiple exciton generation for photovoltaics. By using ultrafast time-resolved spectroscopy we observe competition between electron injection into ZnO and quenching of multiexcitons via Auger recombination. We show that fast electron injection dominates over biexcitonic Auger recombination and multiple electrons can be transferred into ZnO. A kinetic component with time constant of a few tens of picoseconds was identified as the competition between injection of the second electron from a doubly excited QD and a trion Auger recombination. Moreover, we demonstrate that the multiexciton harvesting efficiency changes significantly with QD size. Within a narrow QD diameter range from 2 to 4 nm, the efficiency of electron injection from a doubly excited QD can vary from 30% to 70% in our system.