In quantum metrology, semiconductor single-electron pumps are used to generate accurate electric currents with the ultimate goal of implementing the emerging quantum standard of the ampere. Pumps based on electrostatically defined tunable quantum dots (QDs) have thus far shown the most promising performance in combining fast and accurate charge transfer. However, at frequencies exceeding approximately 1 GHz the accuracy typically decreases. Recently, hybrid pumps based on QDs coupled to trap states have led to increased transfer rates due to tighter electrostatic confinement. Here, we operate a hybrid electron pump in silicon obtained by coupling a QD to multiple parasitic states and achieve robust current quantization up to a few gigahertz. We show that the fidelity of the electron capture depends on the sequence in which the parasitic states become available for loading, resulting in distinctive frequency-dependent features in the pumped current.