Poly (lactic acid) (PLA) suffers from poor melt strength and slow crystallization kinetics, hindering its application in various polymer processing processes like injection molding, blow molding etc. Chain extension and addition of nucleating agents are commonly used to overcome these problems. Recently it has been shown that reactive modification of PLA in the presence of a free radical initiator and a multifunctional coagent results in significantly improved melt strength, while at the same time inducing a nucleating effect. In this work melt state peroxide mediated reactive extrusion of PLA is implemented in the presence of different coagents: triallyl trimesate (TAM), trimethylol propanetrimethacrylate (TMPTMA), trimethylol propanetriacrylate (TMPTA), and pentaerythritol triacrylate (PETA). Oscillatory, extensional, thermal, and molecular weight characterizations were performed to investigate the effect of reactive extrusion on PLA. The types and amount of coagents and peroxide dosed was optimized to prepare formulations with increased melt strength and improved thermal properties. The chain branching and thermal properties of the reactively modified formulations were found be dependent on the type and amount of coagent dosed, with TAM being the most efficient in incorporating both chain branching and improving the thermal properties of PLA.