Many overlay multicast systems proposed in recent years focus on designing an optimized tree for a single data source. They cannot be extended to any-source multicasting because one tree per source is too costly. The existing P2P (peer-to-peer) systems that allow many data sources have high maintenance overhead and lack the flexibility in supporting host diversity. This paper proposes an any-source capacity-constrained overlay multicast service based on a non-DHT (distributed hash table) overlay network specifically suitable for the purpose of multicast. The nodes have different capacities in supporting different numbers of direct children during a multicast session. No explicit multicast trees are maintained on top of the overlay. This paper presents two distributed multicast algorithms that are able to deliver a multicast message from any source to all nodes in the expected O(log_cn) hops, which is asymptotically optimal, where c is the average node capacity and n is the number of members in a multicast group.