Universal wraps are used in the construction of a container centerbody. The wraps may take the form of a top and bottom wrap with complementary stacking patterns, in which the wraps create the centerbody. The wraps permit stacking of different-style containers regardless of which container is positioned as the bottom container. The universal wraps may include curved edge portions to seamlessly and aesthetically blend in with a side panel of the container. The stacking patterns of the wraps may take different forms with various shaped protuberances and recessed portions. Further, one or more of the wraps may have isolation features attached to or integrally formed with an interior surface of the wrap.