This work investigates the design of Hybrid Automatic Repeat Request (HARQ) strategies for downlink Rate-Splitting Multiple Access (RSMA). The existence of private and common stream as well as their conditioning for Successive Interference Cancellation (SIC), gives rise to an expanded set of opportunities for retransmission of failed packets. Specifically, we devise a scheme in which the retransmissions are scheduled through the common stream, which offers a higher success probability. With this, the common stream needs to carry both new and retransmitted bits, which leads to a layered HARQ (L-HARQ) strategy which is capable of trading off throughput and reliability. Simulation results demonstrate that the devised HARQ scheme outperforms RSMA with conventional HARQ, where each retransmission is handled independently through its own stream. It also helps in closing the throughput gap between HARQ and Adaptive Modulation and Coding (AMC) in the high SNR regime while also achieving a decreased Packet Error Rate (PER) and a lower latency.