The application of non-orthogonal multiple access (NOMA) to multi-layer multicast video streaming is envisioned to address the explosively growing demand for capacity which is dominated mostly by multimedia content. In this paper, a joint power allocation and subgrouping scheme is developed to enhance the performance of NOMA-based multi-layer multicast systems. An optimization problem is formulated to maximize the overall sum multicast rate whilst satisfying the maximum transmission power and proportional rate constraints. Due to the complexity of the optimization problem, we first derive two power allocation techniques for the 2-layer case considering arbitrary subgrouping which are based on the iterative implementation and closed-form analysis, respectively. We then generalize the low-complexity closed-form solution for the general multi-layer case. This scheme successively allocates power to each layer stream while assuring that the minimum target rate and proportionality are guaranteed, particularly for the transmission rate of the high-priority base layer stream. A sub-optimal joint power allocation and subgrouping scheme is also designed by incorporating the power allocation scheme into the proposed iterative subgrouping techniques. Simulation results show the effectiveness of the power allocation and subgrouping schemes in enhancing the sum multicast rate performance. In addition, the proposed power allocation scheme ensures substantially higher rates for the base layer stream, which is crucial in robust delivery of standard quality video to all users.