Scalable quantum photonic technologies require the simultaneous production of highly indistinguishable multi-photon states with high probability. This need may be met, and the output probability significantly increased by multiplexed sources, which channel numerous low-probability heralded single-photon sources into a specified output mode using time or spatial multiplexing. However, conventional methods merely replicate these multiplexing units when scaled to multiple output modes, which is fundamentally inefficient because it discards many valid multi-photon events. To address this, we propose and experimentally demonstrate a novel multiplexing source architecture based on a multi-input/multi-output switching network, which can utilize combinatorial photon events. A super-exponential enhancement in multi-port single-photon creation is revealed by theoretical analysis, which significantly reduces the number of heralded single-photon sources needed. We demonstrate multiplexing with two output ports, supported by four integrated heralded single-photon sources. Our strategy has a generation probability of 1.60 times that of conventional methods and 2.58 times that of implementations without multiplexing. This multi-port multiplexed method opens a new avenue for establishing a solid foundation for advanced multi-photon quantum interference and large-scale quantum information processing.