Digital paintings are often created by compositing semi-transparent layers using various advanced color-blend modes, such as "color-burn," "multiply," and "screen," which can produce interesting non-linear color effects. We propose a method of decomposing an input image into layers with such advanced color blending. Unlike previous layer-decomposition methods, which typically support only linear color-blend modes, ours can handle any user-specified color-blend modes. To enable this, we generalize a previous color-unblending formulation, in which only a specific layering model was considered. We also introduce several techniques for adapting our generalized formulation to practical use, such as the post-processing for refining smoothness. Our method lets users explore possible decompositions to find the one that matches for their purposes by manipulating the target color-blend mode and desired color distribution for each layer, as well as the number of layers. Thus, the output of our method is a layered, easily editable image composition organized in a way that digital artists are familiar with. Our method is useful for remixing existing illustrations, flexibly editing single-layer paintings, and bringing physically painted media (e.g., oil paintings) into a digital workflow.