Sustainable and efficient separation technologies are essential for minimizing the environmental impact of the chemical and pharmaceutical industries. Membranes with stability in solvents and precise molecular separation are needed. We report poly(ether ether ketone) (PEEK) membranes engineered for the separation of multicomponent mixtures of active pharmaceutical ingredients (API) of different size and polarity. PEEK is highly stable in solvents typically used in the industry even without crosslinking, but the insolubility is a challenge for solution processing and fibers fabrication. We spun PEEK fibers from solutions in methanesulfonic acid through acid-resistant spinnerets designed and fabricated by stereolithography 3D printing, which are not susceptible to corrosion. Membranes with acetonitrile permeance of around 3 ​L ​m−2 ​h−1 bar−1 and over 90 ​% rejection of molecules with 120 ​g ​mol−1 were obtained. We also innovate in providing a comprehensive performance characterization that predicts the efficiency in separating molecule pairs of different size and chemistry, a procedure more representative of industrial applications instead of the commonly used screening with dye molecules, which can be prone to adsorption artefacts. We discuss the transport mechanisms of organic solvents through the membranes providing a comprehensive analysis of experimental results to evaluate the contributions of pore flow, permeant-polymer affinity and friction to the transport.