Multi-photon interference is a cornerstone of photonic quantum technologies including quantum simulation, communication, and metrology. While four-photon interference has been demonstrated using probabilistic parametric down-conversion sources, the intrinsic trade-off between photon generation rate and photon number purity leads to low signal-to-noise ratios, obscuring important interference phenomena. Here, we overcome this limitation by employing a high-efficiency, on-demand quantum dot single-photon source, achieving order-of-magnitude rate enhancements to reveal complex structure within four-photon interference fringes. By combining experiments with theoretical modelling, we identify “deep fringes” where interference minima are insensitive to photon distinguishability, and fringe contrast is instead highly sensitive to multi-photon emission. A Fisher information analysis further demonstrates that these fringes can exhibit phase sensitivity beyond the standard quantum limit, illustrating potential applications in quantum metrology. By resolving features previously masked by noise, our results establish solid-state emitters as a robust platform for precision quantum optical measurements in the multi-photon regime.