Recently, a new multi-carrier CDMA (MC-CDMA) system with cyclic-shift orthogonal keying (CSOK) has been proposed and shown to be more spectral and power efficient than conventional MC-CDMA systems. In this paper, a novel extension called the multiplexed CSOK (MCSOK) MC-CDMA system is proposed to further increase the data rate while maintaining a low peak-to-average power ratio (PAPR). First, the data stream is divided into multiple parallel substreams that are mapped into QPSK-CSOK symbols in terms of cyclic shifted Chu sequences. Second, these sequences are repeated, modulated, summed, and placed on IFFT subcarriers, resulting in a constant-modulus multiplexed signal that preserves the desired orthogonality among substreams. The receiver performs frequency-domain equalization and uses efficient demultiplexing, despreading, and demapping schemes to detect the modulation symbols. Furthermore, an alternate MCSOK system configuration with high link quality is also presented. Simulations show that the proposed MCSOK system attains lower PAPR and BER, as compared to conventional MC-CDMA system using Walsh codes. Under a rich multipath environment, the high link quality configuration exhibits excellent performance with both diversity gain and MCSOK modulation gain.