The production of biocomposites based on natural fiber waste and biopolymers is constantly increasing because of their renewability, biodegradability, and the accordance with the circular economy principles. The aim of this work is to contrast the disadvantages in the production of biocomposites, such as reduction of molecular weight through the use of biobased chain extenders. For this purpose, epoxidized soybean oil (ESO) and dicarboxylic acids (DCAs) were used to contrast the slight chain scission observed in a poly(lactic acid) (PLA)/poly(butylene succinate-co-adipate) (PBSA) binary blend caused by the melt mixing with hazelnut shell powder (HSP). Two different dimensions of HSPs were considered in this study as well as different concentrations of the ESO/DCA system, comparing succinic acid and malic acid as dicarboxylic acids. Melt viscosity parameters, such as torque and melt volume rate (MVR), were measured to investigate the chain extender effect during the extrusion. In addition, the reactivity of the ESO/DCA system was investigated through infrared spectroscopy. The effect of chain extenders on thermal properties, in particular on the crystallinity of PLA, and on mechanical properties of final biocomposites was investigated to understand their potentialities in industrial application. Results of this study evidenced a modest increase in melt viscosity due to ESO/malic acid chain extension system, but only for the HSP with the lower dimension (so the higher surface area) and adding 0.5 wt.% of ESO/malic acid. Thus, the slight chain scission of polyesters, not significantly affecting the final properties of these biocomposites, is the most relevant effect that was revealed in this complex reactive system.