Non-signaling correlations, which (strictly) include quantum correlations, provide a tractable path to explore the potential impact of quantum nonlocality on the capacity of classical communication networks. Motivated by a recent discovery that certain wireless network settings benefit significantly from non-signaling (NS) correlations, various generalizations are considered. First, it is shown that for a point to point discrete memoryless channel with a non-causal channel state information at the transmitter (CSIT), the NS-assisted Shannon capacity matches the classical (without NS assistance) capacity of the channel for the setting where the state is also made available to the receiver. The key insight is summarized as 'virtual signaling of CSIT via NS-assistance' and is supported by further results as follows. For a discrete memoryless 2-user broadcast channel (BC), the Shannon capacity region with NS-assistance available only between the transmitter and User 1, is found next. Consistent with the aforementioned key insight, the result matches the classical capacity region for the setting where the desired message of User 2 is made available in advance as side-information to User 1. The latter capacity region is known from a result of Kramer and Shamai. Next, for a semi-deterministic BC, the Shannon capacity region with full (tripartite) NS-assistance is shown to be the same as if only bipartite NS-assistance was available between the transmitter and the non-deterministic user. Bipartite NS-assistance between the transmitter and only the deterministic user, does not improve the capacity region relative to the corresponding classical setting. Finally, the analysis is extended to a K-user BC with full NS-assistance among all parties.