Joint Photographic Experts Group (JPEG) achieves data compression by quantizing Discrete Cosine Transform (DCT) coefficients, which inevitably introduces compression artifacts. Most existing JPEG quality enhancement methods operate in the pixel domain, suffering from the high computational costs of decoding. Consequently, direct enhancement of JPEG images in the DCT domain has gained increasing attention. However, current DCT-domain methods often exhibit limited performance. To address this challenge, we identify two critical types of correlations within the DCT coefficients of JPEG images. Building on this insight, we propose an Advanced DCT-domain JPEG Quality Enhancement (AJQE) method that fully exploits these correlations. The AJQE method enables the adaptation of numerous well-established pixel-domain models to the DCT domain, achieving superior performance with reduced computational complexity. Compared to the pixel-domain counterparts, the DCT-domain models derived by our method demonstrate a 0.35 dB improvement in PSNR and a 60.5% increase in enhancement throughput on average. The code will be made publicly available.