Novel multi-component composites composed of the biodegradable polymer poly(ethylene adipate) (PEA), the water-soluble polymer poly(ethylene oxide) (PEO), poly(vinyl acetate) (PVAc), and a supramolecular-like inclusion complex (IC) made by α-cyclodextrin (α-CD) and poly(ε-caprolactone) (PCL) (coded as PCL–CD–IC) are discussed in this work. The PCL–CD–IC was used to increase the crystallization rate of the miscible PEA/PEO/PVAc ternary blend that crystalized slower than neat PEA. Higher resolution SEM and TEM images displayed that PCL–CD–IC did not assemble notably in the quaternary composites. For the results of isothermal crystallization, the analysis of the Avrami equation demonstrated that the rate constant k increased with the addition of PCL–CD–IC in the composites, suggesting that PCL–CD–IC provided more nucleation sites to promote the crystallization rate. The nucleation density increased with the addition of PCL–CD–IC, and the amount of spherulite also increased. Wide angle X-ray results showed that the composites displayed similar diffraction patterns to neat PEA, meaning PEO, PVAc, and PCL–CD–IC would not change the crystal structures of PEA in the composites. The PCL–CD–IC, the supramolecular nucleation agent, demonstrated its superior ability to enhance the multi-component composites of biodegradable polymer in this study.