Incorporating AC-type flying capacitors (FC) between series-connected devices is an effective way to enhance the rated voltage for high-power applications based on current source converters (CSCs). Through appropriate modulation and FC voltage control, it is possible to achieve improved DC bus voltage quality with reduced common-mode voltage (CMV) and low dv/dt. On the other hand, the parallel CSC is a popular choice for increasing the system’s rated current to accommodate higher power applications. The use of interleaved modulation techniques can improve the harmonic performance of parallel converters while reducing the need for passive filters. The modular flying capacitor clamped (FCC)-CSC structure can combine these advantages, achieving higher rated power along with improved power quality on both the DC and AC sides. Moreover, the enhanced AC quality contributes to the regulation of FC voltage and further improves the DC-side voltage quality. This paper analyzes the operation principle of the parallel FCC-CSC structure and proposes an interleaved space vector modulation (SVM) method to enhance the harmonic performance of the AC output. Additionally, an optimized zero-state replacement (ZSR) based FC voltage control and a DC-link current balance strategy built on this control are introduced. Simulation and experimental results validate the effectiveness of the proposed methods.