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Patch antennas are among the most popular radiating elements, yet their quasi-2-D structure reduces the degrees of freedom available to tailor their radiation pattern. To overcome this limitation, a possible solution consists in etching on a grounded substrate two concentric radiating elements and combining two modes (one for each element) with proper amplitude/phase relations. Although this technique leads, in principle, to an infinite number of possible configurations (i.e., each patch element can support an infinite number of modes), the theoretical and experimental verifications available in the literature are limited to the first two radiating modes (TM 11 and TM 21 ) of a circular patch antenna. Recently, we have shown that the design of this circular patch can be effectively performed by exploiting the topological properties of vortex fields and, in particular, by controlling the phase singularity exhibited by the higher order right-handed circularly polarized (RHCP) TM 21 mode of the circular patch. Since the number of RHCP higher order modes of a circular patch is infinite, we can in principle deal with an arbitrary number of phase singularity points, whose combined control leads to unprecedented possibilities to shape the radiation pattern of a circular patch. In this article, we present a complete design tool to determine the number and position of phase singularity points arising when combining the RHCP modes of a circular patch antenna and, eventually, manipulate them to synthesize the required radiation pattern. As a realistic application example, we show how the proposed tool can be used to effectively design a single antenna whose radiation pattern can be properly tailored to switch between two different states, i.e., a sector and a saddle shape, widely used in base stations for mobile and satellite communications, respectively.