Multicasting, where a base station (BS) wishes to convey the same message to several user equipments (UEs), represents a common yet highly challenging wireless scenario. In fact, guaranteeing decodability by the whole UE population proves to be a major performance bottleneck since the UEs in poor channel conditions ultimately determine the achievable rate. To overcome this issue, two-phase cooperative multicasting schemes, which use conventional multicasting in a first phase and leverage device-to-device (D2D) communications in a second phase to effectively spread the message, have been extensively studied. However, most works are limited either to the simple case of single-antenna BS or to a specific channel state information at the transmitter (CSIT) setup. This paper proposes a general two-phase framework that is applicable to the cases of perfect, statistical, and topological CSIT in the presence of multiple antennas at the BS. The proposed method exploits the precoding capabilities at the BS, which enable targeting specific UEs that can effectively serve as D2D relays towards the remaining UEs, and maximize the multicast rate under some outage constraint. Numerical results show that our schemes bring substantial gains over traditional single-phase multicasting and overcome the worst-UE bottleneck behavior in all the considered CSIT configurations.