Crystals with curved diffracting planes have been investigated as high-efficiency optical components for the realization of a Laue lens for satellite-borne experiments in astrophysics. Curved crystals implementing the quasi-mosaic effect, namely an effect of crystalline anisotropy, are able to focus an X-ray beam to a size far smaller than that of the diffracting element, in turn increasing the focusing power of a Laue lens. This work provides first results about the feasibility of a self-standing stack composed of quasi-mosaic crystals. Stacking of crystalline lamellae is a solution to overcome the thickness limitation in existing self-standing quasi-mosaic crystals. Ten thin silicon crystalline lamellae were stacked, and then the planes affected by the quasi-mosaic effect were tested by polychromatic X-ray diffraction. The multicrystal behaved as one diffracting element, yielding a broad and smooth diffraction profile. The effective realization of a quasi-mosaic multicrystal opens up the prospective of building a Laue lens with a large integrated reflectivity, which leads to a high sensitivity, a necessary condition for the observation of celestial X-ray sources via a Laue lens.