Communication over a random multiple-access (RMA) broadcast channel with multiple reception capability is considered. Multiple reception refers to the assumption that a collision is defined as the simultaneous transmission of more than d packets, where d>or=2. In most previous studies of RMA channels, it was assumed that d=1, that is, whenever more than one source tries to use the same slot, a collision occurs, and all the messages involved must be retransmitted. In practice, however, it might be possible to construct RMA systems where simultaneous transmission of d or fewer packets, where d>or=2, is successful. In this work, the author presents conflict resolution algorithms and determine lower bounds to the capacity of such RMA channels for many different feedback models. It is shown that the packet transmission rates (throughput) reported previously can be achieved under much less restricted feedback models.>