A new ultrafiltration technique based on a multimembrane stack has been developed to fractionate solutes closer in size than conventionally possible. The technique is illustrated here by obtaining a pure protein product from a binary protein mixture. By employing membranes in series without any gaskets or spacers in-between, ultrafiltration is carried out to separate two proteins relatively close in molecular weight or size. Flat regenerated cellulose membranes, polyethersulfone membranes or the like, of at least substantially the same molecular weight cutoff (MWCO) are stacked together in the desired number, and ultrafiltration takes place. The membrane rejection of a protein is amplified with each additional membrane, ultimately resulting in a completely rejected species. Complete purification of the more permeable protein is achieved regardless of the physicochemical condition which may be optimal or suboptimal for selective separation by a single membrane.