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We study the Casimir effect in a system composed of two Weyl semimetals (WSMs) separated by a gap filled with a chiral medium. We calculate the optical response of the material to chiral photons in order to calculate the Casimir force. We find that if the medium between the two WSMs is a Faraday material, a repulsive Casimir force can be obtained. The magnitude of this repulsive force is found to be greatly enhanced at distances of a few microns, when experimentally accessible parameters are used. Moreover, in the system under consideration various parameters can be modified. Some of them are intrinsic to the materials employed (the absolute value of the Hall conductivity of the WSM, the Verdet constant of the Faraday material), while some of them can be manipulated externally even for a fixed sample, such as the external magnetic field and the orientation of the plates which determines the sign of their conductivity. Suitable combinations of these parameters can be used to switch from attraction to repulsion, and to place the trapping distance, in which no force acts on the plates, at any desired distance between them.