In order to toughen Poly(lactic) acid and binary blends with low PBAT content while maintaining a high biodegradability of the final material, poly(lactic) acid (PLA)/poly(butylene-adipate-co-terephthalate) (PBAT)/ polyolefin elastomer grafted with glycidyl methacrylate (POE-g-GMA) extruded ternary blends have been investigated in this work from a thermal, mechanical, and rheological point of view. The two elastomers have been added in different amounts as dispersed phases into the PLA matrix, paying attention to the final objective: the design of a 90% biodegradable formulation according to EN 13432. These ternary blends exhibited improved impact properties but still low elongation at break. Consequently, to the ternary composition with the best compromise of PLA quantity, biodegradability and thermo-mechanical properties (81 wt.% PLA, 9 wt.% PBAT, and 10 wt.% POE-g-GMA) a small quantity (10 wt.%) of a biobased plasticizer was added in order to further increase the impact properties in parallel with the tensile flexibility. Two types of plasticizers were investigated, one not reactive [Acetyl Tributyl Citrate (ATBC)], and one reactive [Glycidyl ether (EJ-400)]. A micromechanical study, in order to investigate the toughening mechanism of these systems, was carried out on the final formulations. They were also examined by dilatometric tests and elastoplastic fracture mechanics correlating the data obtained to the morphology and to the rheological properties. In conclusion, the best compromise between impact, tensile properties and biodegradability content was achieved using the reactive plasticizer (EJ-400) whose interaction with the matrix is confirmed by the FT-IR analysis.