Strict TCP-friendliness is a problematic issue that discourages multicast deployment on the Internet. In this paper, we therefore propose a new design of multi-rate multicast congestion control (MR-MCC) by revising our previous proposed MR-MCC protocol, namely explicit rate adjustment (ERA). In the new design, a multicast-supportive TCP-friendliness bandwidth allocation is used at intermediate nodes (routers) to motivate multicast deployment by giving more bandwidth to ERA without starving TCP. At the end node, an explicit reception rate adjustment algorithm is used. The receiver adjusts its reception rates according to the network conditions using packet-pair probe (PP). The implementation of our new ERA is done on the network simulator 2 (ns2). We demonstrate via simulations that the new ERA could provide responsiveness, fairness and the motivation for multicast deployment.