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This article presents a unified framework analysis for the performance of reconfigurable intelligent surface (RIS)-aided coordinated non-orthogonal multiple access (C-NOMA) systems where the discrete phase-shift alignment and imperfect successive interference cancellation (SIC) are investigated. This framework yields double opportunities to enhance users' performance via RIS and dedicated relay transmission. To assess the system characteristic, the users' outage probability (OP) and ergodic capacity (EC) expressions are evaluated and derived in terms of approximate closed-form and asymptotic expressions. Numerical results validate our derivations and show that: i) expanding the number of RISs element implementations can significantly improve the users' OP, and ii) the RIS-aided C-NOMA system achieves a superior EC improvement compared to RIS-orthogonal multiple access (OMA) and conventional C …