In one embodiment, a particular PE device of a plurality of multi-homing PE devices between a core network and a local network determines a subset of traffic for which the particular PE device is responsible. The particular PE also establishes, with itself as root, a multicast tree within the local network for underlay multicast groups. Traffic received at the particular PE from the core network is admitted into the local network only if the core traffic corresponds to the subset of traffic for which the particular PE device is responsible (and mapped into one of the underlay multicast groups for which the particular PE device is the root). Also, multicast traffic received at the particular PE from the local network is forwarded into the core network only if the multicast traffic corresponds to the subset of traffic for which the particular PE device is responsible.