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Reconfigurable magnetic tunnel diodes and transistors are a new concept in spintronics. The realization of such a device requires the use of materials with unique spin-dependent electronic properties such as half-metallic magnets (HMMs) and spin-gapless semiconductors (SGSs). Quaternary Heusler compounds offer a unique platform to design within the same family of compounds HMMs and SGSs with similar lattice constants to make coherent growth of the consecutive spacers of the device possible. Employing state-of-the-art first-principles calculations, we scan the quaternary Heusler compounds and identify suitable candidates for these spintronic devices combining the desirable properties: (i) HMMs with sizable energy gap or SGSs with spin gaps both below and above the Fermi level, (ii) high Curie temperature, (iii) convex hull energy distance less than 0.20 eV, and (iv) negative formation energies. Our results pave the way for the experimental realization of the proposed magnetic tunnel diodes and transistors.