A multicode transmission (MC) system can transmit multiple data streams at one time. However, the amplitude of the transmission signal has sharp fluctuations. To avoid this problem, constant amplitude (CA) signaling schemes were studied, and some MC systems were developed such as the MC system with CA signaling (MC-CA) and the parallel combinatory MC system with CA signaling (PCMC-CA). In this paper, extension systems of PCMC-CA system are developed. In particular, two demodulation methods are discussed for the extension systems. Then, the bit error rate (BER) and data transmission rate are theoretically analyzed. The results shows that the extension systems has a better performance than the MC-CA system in both of the BER and data transmission rate.