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Free-space optical (FSO) communications has the potential to revolutionize wireless communications due to its advantages of inherent security, high-directionality, high available bandwidth and small physical footprint. The effects of atmospheric turbulence currently limit the performance of FSO communications. In this letter, we demonstrate a system capable of indiscriminately suppressing the atmospheric phase noise encountered by independent optical signals spread over a range of 7.2 THz (encompassing the full optical C-Band), by actively phase stabilizing a primary optical signal at 193.1 THz (1552 nm). We show ~30 dB of indiscriminate phase stabilization over the full range, down to average phase noise at 10 Hz of -39.6 dBc/Hz when using an acousto-optic modulator (AOM) as a Doppler actuator, and -39.9 dBc/Hz when using a fiber-stretcher as group-delay actuator to provide the phase-stabilization system's feedback. We demonstrate that this suppression is limited by the noise of the independent optical signals, and that the expected achievable suppression is more than 40 dB greater, reaching around -90 dB/Hz at 10 Hz. We conclude that 40 Tbps ground-to-space FSO transmission would be made possible with the combination of our stabilization system and other demonstrated technologies.