Nine-switch Inverters (NSIs) have been proposed to accommodate the independent control of dual AC motors or in six-phase drives. This topology reduces the number of active switches by 25% compared with conventional Voltage Source Inverter (VSI). However, it has a main conceptual shortcoming of voltage gain limitations. The voltage gains of both outputs are low, and their values depend on the phase angle between the two three-phase voltage output sets. This paper introduces a Quasi-Z Source NSI (QZS-NSI) topology to overcome voltage gains shortcomings of NSIs. Although a body of research for conventional three-phase QZS-VSI has been undertaken, corresponding discussions for all the impedance network based NSI are still scarce and complicated. This paper proposes a simple carrier-based PWM approach to modulate the QZS-NSI in both common-frequency and different-frequency modes of operations. Accordingly, four PWM schemes are introduced with simple, maximum and constant boost control methods. The operating principles and performance criteria of each scheme are introduced and compared. The feasibility of the proposed modulation schemes is confirmed by the simulation results which show good accordance with the theoretical analysis. Furthermore, the presented strategy can be extended to other types of impedance network-based NSIs.