Secure documents often comprise an information layer that is hard to reproduce. Moiré techniques for the prevention of counterfeiting rely on the superposition of an array of transparent lines or microlenses on top of a base layer containing hidden information. Level-line moirés consist of shapes that appear to be beating upon relative translation of a revealing grating on top of a base, in which the desired information is encoded. Usually, the base only contains the information corresponding to one moiré. In order to increase the difficulty of counterfeiting, we use tessellations to incorporate two or more moirés within the same layer. With the method we propose, the information corresponding to up to seven level-line moirés can be embedded within a single base layer. The moirés are recovered with a revealer printed on a transparency or with an array of cylindrical lenses. This method is general and can be extended to other fabrication technologies.