This paper proposes a new model of high capacity carrier interferometry/multicarrier code division multiple access (CI/MCCDMA) system through the simultaneous support of high and low data rate transmission using odd and even subcarriers. Reduction in peak-to-average power ratio (PAPR) is achieved through the phase shift of even (odd) CI code using odd (even) sub-carriers by an amount of π/2 and odd (even) CI code using odd (even) sub-carriers by -π/2, all angles measured with respect to the orthogonal codes supporting high data rate transmission. The CI code optimization is done for further reduction in PAPR values. Specifically, assuming a frequency selective Rayleigh-fading channel, bit error rate (BER) at receiver is improved through the cancelation of MAI (multiple access interference) at subcarriers level using PIC (parallel interference cancelation) at reduced computation cost. Finally, the system is optimized with respect to the number of subcarriers, number of users (capacity) and signal-to-noise ratio (SNR) using GAs (Genetic Algorithms) to achieve an acceptable set of values for BER, PAPR and average data rate (ADR).