The formation of all-organic dual spin valves (DSVs) with three organic spin-selective layers, that is, spin-injection, spin-detection, and an additional spin-filtering layer at the intermediate, is reported. As spin-selective layers, manganese- and cobalt phthalocyanines, which are well-known single-molecule magnets, are used in their immobilized forms, so that all-organic DSVs can be prefabricated for characterization. The three spin-selective layers have provided four configurations with at most two spin-flip interfaces enforcing spin-flipping at the two nonmagnetic organic spacer layers, for which copper phthalocyanine is used. Since a couple of the four configurations have exhibited similar resistivities, the degeneracy in the resistive-states is broken through asymmetric spin-injection and spin-detection layers and also through asymmetric thickness of the nonmagnetic spacer layers. When both the spin-flip interfaces are made operative independently, a 2-bit logic with four distinct resistive states can be achieved.