An injection mold assembly for manufacturing multiple-component articles includes opposed first and second mold halves and mold cores carried by the first mold half. Each of the mold cores is mounted for rotation between a first position and a second position about an axis of rotation. The mold halves are mounted for movement in reciprocal directions along an axis of reciprocation between an open position and a closed position forming molding cavities between the mold cores and the second mold halves. The axes of rotation of the mold cores are different from one another.