In this paper, we propose a method for high-capacity reversible data hiding in compressible encrypted images. While reversible data hiding in encrypted images (RDH-EI) has been actively studied, most previous research in this field has focused on the hiding capacity. We previously proposed an RDH-EI method that achieves both a high hiding capacity and high compression performance simultaneously. The method can effectively compress marked encrypted images using lossless image coding standards with a hiding capacity of up to about 1~bpp. In addition, there is an option to decrypt marked encrypted images without data extraction, so marked images can be obtained, still containing the embedded data, i.e., payload. Without losing the advantages of the previous method, we propose an extended method, in which the highest frequency bin is constantly used for data hiding. Consequently, the hiding capacity is further enhanced up to 2.45 bpp for each color component in the proposed method. Through our experiments, we prove the superiority of the proposed method.