Control of electromagnetic waves using engineered materials is very important in a wide range of applications, therefore there is always a continuous need for new and more efficient solutions. Known natural and artificial materials and surfaces provide a particular functionality in the frequency range they operate but cast a "shadow" and produce reflections at other frequencies. Here, we introduce a concept of multifunctional engineered materials that possess different predetermined functionalities at different frequencies. Such response can be accomplished by cascading metasurfaces (thin composite layers) that are designed to perform a single operation at the desired frequency and are transparent elsewhere. Previously, out-of-band transparent metasurfaces for control over reflection and absorption were proposed. In this paper, to complete the full set of functionalities for wave control, we synthesize transmitarrays that tailor transmission in a desired way, being "invisible" beyond the operational band. The designed transmitarrays for wavefront shaping and anomalous refraction are tested numerically and experimentally. To demonstrate our concept of multifunctional engineered materials, we have designed and measured a cascade of three metasurfaces that performs three different functions for waves at different frequencies. Remarkably, applied to volumetric metamaterials, our concept can enable a single composite possessing desired multifunctional response.