While it has been shown that backscattering induced phase noise can be suppressed by adopting acoustic-optic-modulators (AOMs) at the local and remote sites to break the frequency symmetry in both directions. However, this issue can not be avoided for conventional fiber-optic multiple-access coherent optical phase dissemination in which the interference of the signal light with the Rayleigh backscattered light will probably destroy the coherence of the stabilized optical signal. We suppress the backscattering effect by locally breaking the frequency symmetry at the extraction point by inserting an additional AOM. Here, we theoretically analyze and experimentally demonstrate an add-drop one more AOM approach for suppressing the Rayleigh backscattering within the fiber link. Near-complete suppression of backscattering noise is experimentally confirmed through the measurement the elimination of a common interference term of the signal light and the Rayleigh backscattered light. The results demonstrate that the Rayleigh backscattering light has a limited effect compared to the residual delay-limited fiber phase noise on the systems performance. Our results also provide new evidence that it is possible to largely suppress Rayleigh and other backscattering noise within a long optical fiber link, where the accumulated phase noise could be large, by using frequency symmetry breaking at each access node to achieve robust multiple-access coherent optical phase propagation in spite of scatters or defects.