Reversible data hiding in encrypted images (RDHEI) is a well-established technique in which additional information is embedded to ensure data imperceptibility and full reversibility. For RDHEI, how to utilize more redundant space to improve the embedding capacity (EC) under the premise of true reversibility is still a challenging task. We propose a separable RDHEI scheme based on multiple predictive compression coding. The image is classified by texture complexity based on gray level co-occurrence matrix. For different blocks, adaptive weight prediction (AWP) and global optimization adaptive weight prediction (GOAWP) are proposed to improve prediction accuracy. More importantly, GOAWP solves the problem of inaccurate prediction of texture block. Furthermore, methods based on pixel difference compression, pixel bit-based difference compression, and block plane-based difference compression are proposed to vacate more embedding space. The proposed scheme is separable. For the content owner, above two predictors and three compression methods are adopted to vacate space for hiding. For the data hider, the secret bits are embedded into the encrypted image by directly replacing the spare bits without obtaining any information of the original image. For the receiver, the desired information can be retrieved according to the key in his/her possession. By taking full advantage of the pixel correlation and multiple predictive compression coding, the proposed method successfully achieves a significant improvement in capacity. Experimental results show that the highest payload of our scheme reaches 3.6185 bpp, which exhibits appreciated EC in comparison with state-of-the-art methods. Security and compression performance is emphasized, where the key space of our scheme is as high as 2 × 10¹⁵ × ∞ × 10¹⁵, the average information entropy of the embedded compressed image is 7.8891, and the correlation coefficients between original images and the compressed and embedded compressed images are close to 0, indicating a weak correlation, thereby greatly improving security.