In this paper, we investigate the throughput performance of single-packet and multi-packet hybrid-automatic repeat request (HARQ) with blanking for downlink non-orthogonal multiple access (NOMA) systems. While conventional single-packet HARQ achieves high throughput at the expense of high latency, multi-packet HARQ, where several data packets are sent in the same channel block, can achieve high throughput with low latency. Previous works have shown that multi-packet HARQ outperforms single-packet HARQ in orthogonal multiple access (OMA) systems, especially in the moderate to high signal-to-noise ratio regime. This work amalgamates multi-packet HARQ with NOMA to achieve higher throughput than the conventional single-packet HARQ and OMA, which has been adopted in the legacy mobile networks. We conduct theoretical analysis for the throughput per user and also investigate the optimization of the power and rate allocations of the packets, in order to maximize the weighted-sum throughput. It is demonstrated that the gain of multi-packet HARQ over the single-packet HARQ in NOMA systems is reduced compared to that obtained in OMA systems due to inter-user interference. It is also shown that NOMA-HARQ cannot achieve any throughput gain with respect to OMA-HARQ when the error propagation rate of the NOMA detector is above a certain threshold.