To support parameter adjustment of an overflow-adjustable hydrocyclone under changing feed conditions, this study evaluated its classification performance and multi-criteria optimization under a range of steady-state operating conditions. Single-factor experiments quantified the effects of feed concentration, feed pressure, and overflow-baffle height on key classification metrics. Among the variables examined, feed concentration produced the largest observed change in overflow fineness. Increasing the feed solids concentration from 28.5% to 51.9% decreased overflow fineness and classification efficiency by 18.34 and 8.35 percentage points, to 77.27% and 55.21%, respectively. To optimize the conflicting responses of overflow fineness, classification efficiency, and underflow yield simultaneously, an orthogonal design was combined with weighted grey relational analysis. Among the original orthogonal runs, A3B3C3 (feed pressure 0.16 MPa, baffle diameter 115 mm, and baffle height 260 mm) produced the highest grey relational grade. Main-effect analysis, however, identified A1B3C3 (feed pressure 0.12 MPa, baffle diameter 115 mm, and baffle height 260 mm) as the preferred factor-level combination. A confirmation experiment at A1B3C3 yielded an underflow yield of 58.62%, an overflow fineness of 88.91%, and a classification efficiency of 61.05%. Under the specified weights, A1B3C3 achieved the highest grey relational grade of 0.8040 among the evaluated conditions and was therefore selected as the preferred multi-response condition. These steady-state comparisons provide a basis for selecting OAHC operating and structural parameters after feed conditions change; transient adjustment performance under continuous fluctuations remains to be evaluated.