We investigate the downlink outage performance of double-RIS-aided non-orthogonal multiple access (NOMA), where a near-BS and a near-users RISs setup are deployed. To extend the coverage to 360 degrees, we deploy a simultaneously transmitting and reflecting RIS (STAR-RIS) structure to improve communication reliability for indoor and outdoor users. New channel statistics for the end-to-end channel with Nakagami-m considering both the conventional-RIS and the STAR-RIS antenna elements features are derived using the moment-matching (MM) technique. The numerical results reveal that the double-RIS setup can outperform the single-RIS designs when the number of elements of STAR- RIS (RS) and conventional RIS (RC) is suitably adjusted. Moreover, the double-RIS setup outperforms the single-RIS design when the link between the base station and the near-user RIS is in good condition. Finally, the proposed analytical equations are accurate under different channel and system configurations.