Three different approaches have been proposed so far for production of highly monochromatic X-rays from a baseline XFEL undulator: (i) single-bunch self-seeding scheme with a four crystal monochromator in Bragg reflection geometry; (ii) double-bunch self-seeding scheme with a four-crystal monochromator in Bragg reflection geometry; (iii) single-bunch self-seeding scheme with a wake monochromator. A unique element of the X-ray optical design of the last scheme is the monochromatization of X-rays using a single crystal in Bragg-transmission geometry. A great advantage of this method is that the monochromator introduces no path delay of X-rays. This fact eliminates the need for a long electron beam bypass, or for the creation of two precisely separated, identical electron bunches, as required in the other two self-seeding schemes. In its simplest configuration, the self-seeded XFEL consists of an input undulator and an output undulator separated by a monochromator. In some experimental situations this simplest two-undulator configuration is not optimal. The obvious and technically possible extension is to use a setup with three or more undulators separated by monochromators. This amplification-monochromatization cascade scheme is distinguished, in performance, by a small heat-loading of crystals and a high spectral purity of the output radiation. This paper describes such cascade self-seeding scheme with wake monochromators. We present feasibility study and exemplifications for the SASE2 line of the European XFEL.