Complete complementary code based direct sequence code division multiple access (CC/DS-CDMA) system has been proposed recently as a potential candidate for beyond the third generation (B3G) mobile communications. This paper addresses the issue on variable capacity property (VCP) of a CC/DS-CDMA system with multiple time slots, pertaining to the multi-rate channel assignment schemes of a CC/DS-CDMA system. In particular, three traffic classes and two dynamic code flock assignment schemes, namely random assignment (RA) and compact assignment (CA), are considered in our study. Simulation results of blocking probability, mean and variance of system capacity, and throughput under different schemes are derived and compared. It is concluded that the VCP of CC/DS-CDMA systems is sensitively affected by different code flock assignment schemes. In general, CA can offer lower blocking probability and more stable system capacity; whereas RA can offer larger mean system capacity and higher throughput when offered traffic is heavy.