We study the problem of maximizing the multicast throughput in a dense multi-channel multi-radio (MC-MR) wireless network with multiple multicast sessions. Specifically, we consider a fully connected network topology where all nodes are within transmission range of each other. In spite of its simplicity, this topology is practically important since it is encountered in several real-world settings. Further, a solution to this network can serve as a building block for more general scenarios that are otherwise intractable. For this network, we show that the problem of maximizing the uniform multicast throughput across multiple sessions is NP-hard. However, its special structure allows us to derive useful upper bounds on the achievable uniform multicast throughput. We show that an intuitive class of algorithms that maximally exploit the wireless broadcast feature can result in very poor worst case performance. Using a novel group splitting idea, we then design two polynomial time approximation algorithms that are guaranteed to achieve a constant factor of the throughput bound under arbitrary multicast group memberships. These algorithms are simple to implement and provide interesting tradeoffs between the achievable throughput and the total number of transmissions used.