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We report the design and characterization of a multiphase quadruple shape memory composite capable of switching between 4 programmed shapes, three temporary and one permanent. Our approach combined two previously reported fabrication methods by embedding an electrospun mat of PCL in a miscible blend of epoxy monomers and PMMA as a composite matrix. As epoxy polymerization occurred the matrix underwent phase separation between the epoxy and PMMA materials. This created a multiphase composite with PCL fibers and a two-phase matrix composed of phase-separated epoxy and PMMA. The resulting composite demonstrated three separate thermal transitions and amenability to mechanical programming of three separate temporary shapes in addition to one final, equilibrium shape. In addition, quadruple surface shape memory abilities are successfully demonstrated. The versatility of this approach offers a large degree of design flexibility for multi-shape memory materials.