Controlling the peak-to-mean envelope power ratio (PMEPR) of multi-carrier code division multiple access (MC-CDMA) transmissions is a notoriously important problem. In this letter, a direct construction of multiple complete complementary codes (CCCs) with inter-set zero cross-correlation zone (ZCCZ) is proposed based on multivariable functions. The presented construction has an advantage over the previous works with regard to the new flexible parameters and low column sequence PMEPR, which may give an extra benefit in fulfilling different requirements and managing PMEPR in MC-CDMA systems with multiple cells. In addition, it turns out that the combination of the constructed CCCs results in a new optimal Z-complementary code set (ZCCS).