We propose and investigate reconfigurable multiple-frequency (MF)-spaced MF-offset flat optical comb generation using an electro-optic (EO) multiple-parallel phase modulator (MP-PM). In the technique, the frequency spacing and offset of the generated comb can be flexibly controlled through the EO modulation process without relying on optical filters, which are configurable at frequencies much beyond the EO modulation bandwidth, e.g., 50, 100 GHz, or higher. In this paper, the driving conditions of the MP-PM for the MF-spaced and MF-offset comb generation with great spectral flatness are analytically clarified and summarized as simple formulas. Repartitioning of the modulator arms is also discussed for flexible comb generation with higher conversion efficiency.