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We generalize the concept of multiuser peer-to-peer (MUP2P) relay networks, where K source-destination pairs communicate through L relays, to that of a multi-group multicasting (MGM) relay network. In the MGM scenario, each source may broadcast its message to a group of multiple users rather than to a single user only. Common distributed beamformer designs for MUP2P relay networks aim to minimize the total transmitted relay power subject to receiver quality-of-service (QoS) constraints. In state-of-the-art techniques, the resulting nonconvex problem is approximated by a convex one which is efficiently solvable using interior point methods. These techniques are shown to be straightforwardly extendable to more general MGM relay networks. However, as the number of receivers increases (which may be typical for the proposed MGM networks where each multicast group may contain many users), these approximations become more and more inaccurate leading to severe performance degradation and problem infeasibility. To avoid this drawback, we propose an iterative method where in each iteration, a convex approximation of the original problem is solved and then adapted to the solution obtained in this iteration. We show that the approximate solution can be successively improved using such iterations. Simulation results show that in scenarios with large numbers of destination users, the proposed method substantially outperforms the state-of-the-art methods developed for MUP2P relay networks.