Screen content images (SCIs) often contain a mix of natural and synthetic image parts. Synthetic sections usually are comprised of uniformly colored areas as well as repeating colors and patterns. In the Versatile Video Coding (VVC) standard, these properties are largely exploited using Intra Block Copy and Palette Mode. However, the Soft Context Formation (SCF) coder, a pixel-wise lossless coder for SCIs based on pattern matching and entropy coding, outperforms the VVC in very synthetic image areas even when compared to the lossy VVC. In this paper, we propose an enhanced VVC coding approach for SCIs using Soft Context Formation. First, the image is separated into two distinct layers in a block-wise manner using a learning-based method with 4 block features. Highly synthetic image parts are coded losslessly using the SCF coder, whereas the rest of the image is coded using VVC. The SCF coder is further modified to incorporate information gained by the decoded VVC layer when encoding the SCF layer. Using this approach, we achieve BD-rate gains of 4.15% on average on the evaluated data sets when compared to VVC.