Employing nanofiltration, a separation of uncharged solutes, monovalent, and bivalent ions from multicomponent aqueous solutions is potentially feasible. Separation is strongly influenced by process parameters as well as the feed properties and membrane characteristics. The aqueous solution in this study includes strategic elements (Ge, Co, Mo, Re) in a wide range of concentrations and varying ionic species. The feed composition mirrors a bioleachate of a German flue dust resulting from copper ore smelting. In a number of cross-flow experiments, the separation performance of eight commercial polymeric nanofiltration membranes was evaluated and the influence of transmembrane pressure, flow velocity, flow regime, recovery, and ionic strength was investigated. It was observed that a high ionic strength (evoked by a high Zn concentration) affects Re retention negatively and decreases permeability. By increasing the transmembrane pressure, the separation selectivity towards Re is enhanced. An almost quantitative Re separation is realized with a cut-off below 200 Da (RO90, NE-90). The utilized NF99HF membrane shows the best results regarding permeability and separation selectivity towards Re, Ge, and Mo.