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Summary: This paper investigates a nonlinear energy scavenging overlay network (NLESON) wherein a primary source (PS) communicates with a primary destination (PD) probably under aid of a secondary source (SS) who communicates with a secondary destination (SD). SS is a power‐constrained device, and thence, its operation relies on energy harvested by a practical nonlinear energy scavenger. To support PS and exploit the harvested energy at most, SS adaptively switches between single and superposition modes where the single mode allows SS to transmit solely its signal with the entire harvested energy and the superposition mode asks SS to transmit both—its signal and amplified primary signal—with different power fractions. Moreover, for increasing the probability of successfully decoding primary signal at PD and SD, which then reduces considerably primary interference on secondary signal in the superposition mode, we leverage both direct channels (PS‐PD and PS‐SD) and apply both signal combining paradigms (maximum ratio combining and selection combining). The outage/throughput performance of the NLESON is assessed quickly through the proposed closed‐form expressions over κ−μ shadowed fading channels. Various results exposed the effectiveness of the aforementioned solutions for the NLESON and their flexibility in controlling system performance. [ABSTRACT FROM AUTHOR]