Method and apparatus for sequentially delivering multiple shots of polymer material to a plurality of mold cavities to form multilayer articles. A first shot of greater than 50% of the total article weight of a first polymer material is simultaneously delivered to a plurality of mold cavities using, at each cavity, a chamber of predetermined volume that is prefilled with the first polymer material. A second shot of no greater than 10% of the total article weight of a second material is simultaneously delivered to all of the cavities beginning subsequent to the step of delivering the start of the first shot delivery step. The second shot of second material is delivered through a manifold channel that fluidly communicates with each cavity, and is injected to all cavities under pressure exerted by a source of the second material that is common to all of the plurality of cavities.