The compound, Ca3CoRhO6, containing magnetic Co-Rh chains intervened by Ca ions, has been known to be one of the few exhibiting partially disordered antiferromagnetic structure (PDA) due to geometrical frustration. Here, we report the influence of partial replacement of Ca by Y on the magnetic anomalies by investigating the solid solution, Ca(3-x)Y(x)CoRhO6 by bulk measurements. There are profound changes in the magnetic behavior, the most notable one being that the features attributable to spin-chain magnetism and PDA structure get suppressed dramatically by a small replacement of Ca by Y (x= 0.15), despite the fact that the magnetic chain is not disrupted. This finding suggests that this compound is on the verge of PDA-structural-instability.