Poly (lactic acid) is an industrially mature, bio-sourced and biodegradable polymer. However, current applications of this eco-friendly material are limited as a result of its brittleness and its poorly melt properties. One of the keys to extend its processing window is to melt strengthen the native material. This paper considers the chain extension as a valuable solution for reaching such an objective. An additive based on epoxy-functionalized PLA was employed during reactive extrusion. The reaction times as a function of chain extender ratios were determined by monitoring the melt pressure during recirculating micro-extrusions. Once residence times were optimized, reactive extrusion experiments were performed on a twin screw extruder. Size exclusion chromatography provided information about the molecular weight distributions (MWD) of the modified PLAs and revealed the creation of a high molecular weight shoulder. The rheological experiments highlighted the enhancement of the melt properties brought about by the chain extension. Shear rheology revealed some enlarged and bimodal relaxation time spectra for the extended materials which are in accordance with the MWD analysis. Such a modification directly amplified the shear sensitivity of modified PLAs. Regarding the rheological temperature sensitivity, it was found to be decreased when the chain extender content is raised as shown from the Arrhenius viscosity fit. The reduction of the polar interactions from neat to highly chain-extended PLAs is here proposed to explain this surprising result. Chain extension was also found to impact on the elongational melt properties where strain hardening occurred for modified PLAs. Investigation of the chain extension architecture was made from the rheological data and revealed a long-chain branched topology for the modified PLAs.