Methods and systems for co-extruding multiple polymeric material flow streams into a mold having a plurality of cavities to produce a plurality of multi-layer polymeric articles each having a consistent coverage of an interior core layer are disclosed herein. In an example method, a flow rate of a first skin material into a cavity is individually controlled for each cavity before initiation of co-injection of a second core material into the cavity, which may address inconsistent interior core layer coverage for articles from different cavities.