The present invention provides a high-resolution membrane-based method for removing a virus from a manufactured protein-containing solution, the method being particularly characterized by its capacity to be performed quickly (i.e., as measured by flux) and efficiently (i.e., as measured by log reduction value, LRV). Towards such results, the present invention employs a plurality (i.e., greater than 2) of interfacially-contiguous asymmetric ultrafiltration membranes, the foremost of which is oriented with its "tight side" facing downstream. The present invention also provides a filtration capsule, useful in the conduct of the method, comprising a pleated tube formed of three interfacially-contiguous asymmetric ultrafiltration membranes.