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This paper considers the multiantenna broadcast channel without transmit-side channel state information. For this channel, it has been known that when all receivers have channel state information (CSIR), the degrees of freedom (DoFs) cannot be improved beyond what is available via time-division multiple access. The same is true if none of the receivers possess CSIR. This paper shows that an entirely new scenario emerges when receivers have unequal CSIR. In particular, orthogonal transmission is no longer DoF optimal when one receiver has CSIR and the other does not. A multiplicative superposition is proposed for this scenario and shown to attain the optimal DoFs under a wide set of antenna configurations and coherence lengths. Two signaling schemes are constructed based on the multiplicative superposition. In the first method, the messages of the two receivers are carried in the row and column spaces of a matrix, respectively. This method works better than orthogonal transmission while reception at each receiver is still interference-free. The second method uses coherent signaling for the receiver with CSIR, and Grassmannian signaling for the receiver without CSIR. This second method requires interference cancellation at the receiver with CSIR, but achieves higher DoF than the first method.