In traditional CSMA/CA-based MAC designs supporting successive interference cancellation (SIC), channel utilization is inefficient, because the inherited CSMA/CA-style contention approach often forces the whole channel to remain idle and the early released channel is not utilized. In this paper, we propose Multi-CQ, which is the first software-defined networking (SDN)-based MAC design for wireless LANs that supports SIC and significantly improves the channel utilization. Multi-CQ, adopting SDN's functional separation idea and OFDMA, makes contention and data transmission be executed over two subchannels independently and concurrently, where the superposition coding are used for decoding combined signals, and multiple CQs (contention queues) are introduced to coordinate the concurrency. This concurrent execution greatly reduces the waste in channel contention. Next, adopting SDN's central control idea, Multi-CQ controller selects nodes who can finish their frame transmissions in almost equal time, thereby improving the channel utilization. Finally, we develop a theoretical model to optimize bandwidth allocation for channel contention and data transmission. Extensive simulations verify the effectiveness of our design and the accuracy of our theoretical model. This study is also helpful to better design wireless MAC protocols supporting other advanced functionalities such as MU-MIMO.