Four-wave parametric amplification (FWPA) in hybrid quantum systems holds substantial promise for advancing high-performance photonic devices, yet achieving ultrahigh probe-wave gain while preserving tunability remains a key challenge. To address this challenge, we investigate a coupled system consisting of a semiconductor quantum dot (SQD) and a metallic nanoshell (MNS) system, where the MNS comprises a metallic core and a dielectric shell. We utilize nonlinear polarization to analyze the spatial propagation effect and derive an analytical expression for the probe-wave gain $G$ that extends beyond the dipole approximation. Our key findings show that in the strong exciton-plasmon coupling regime, the probe-wave gain $G$ exhibits weak dependence on pump intensity. Importantly, significant parametric amplification is achievable by simply adjusting either the interparticle distance between the SQD and MNS or the dielectric shell thickness of the MNS. Notably, when quasi or perfect collinear phase matching is satisfied, the FWPA-mediated $G$ exhibits an extraordinary tunable range, spanning from $2.0\times {10}^{-5}$ to $1.23\times {10}^{16}$. These findings provide a new pathway for the design of high-performance parametric oscillators and signal amplifiers.

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• Nonlinear optics