Biodegradable blends based on plasticized poly(lactic acid) PLA and thermoplastic starch (TPS) have been obtained. The influence of the PLA plasticizer as a compatibility agent has been studied by using two different plasticizers such as neat oligomeric lactic acid (OLA) and functionalized with maleic acid (mOLA). In particular, the morphological, thermal, and mechanical properties have been studied as well as the shape memory ability of the melt-processed materials. Therefore, the influence of the interaction between different plasticizers and the PLA matrix as well as the compatibility between the two polymeric phases on the thermally-activated shape memory properties have been studied. It is very interesting to use the same additive able to act as both plasticizer and compatibilizer, decreasing the glass transition temperature of PLA to a temperature close to the physiological one, obtaining a material suitable for potential biomedical applications. In particular, we obtain that OLA-plasticized blend (oPLA/TPS) show very good thermally-activated capability at 45 °C and 50% deformation, while the blend obtained by using maleic OLA (moPLA/TPS) did not show shape memory behavior at 45 °C and 50% deformation. This fact is due to their morphological changes and the loss of two well-distinguished phases, one acting as fixed phase and the other one acting as switching phase to typically obtain shape memory response. Therefore, the thermally-activated shape memory results show that it is very important to make a balance between plasticizer and compatibilizer, considering the need of two well-established phases to obtain shape memory response.