A multiple opening, counter-flow plate type exchanger is manufactured by repeatedly folding and joining one strip of membrane to form a core composed of a multitude of membrane layers with a plurality of inlet and outlet openings or fluid passageways configured in an alternating counter-flow arrangement. Methods for manufacturing such multiple opening cores are described. An integrated, modular, and stackable plastic manifold that is formed by ultrasonically welding plastic sheet stock is described. Multiple opening cores comprising water-permeable membranes can be used in a variety of applications, including heat and water vapor exchangers. In particular, they can be incorporated into energy recovery ventilators (ERVs) for exchanging heat and water vapor between air streams directed into and out of buildings, automobiles, or other Industrial processes.