To implement K-user multi-rate multi-power transmission in non-orthogonal multiple access systems with successive interference cancellation, a repeat accumulator code serially concatenated with a spreading is employed for each user to implement a variable, low-rate coding. A joint rate and power optimization (RPO) is proposed to maximize the sum rate with error free decoding. Numerical results show that our proposed codingspreading scheme with joint RPO, supporting the multi-rate transmission with the same structure of encoder, approaches the Shannon limit.