Recently, there has been immense interest in using biodegradable polymers to replace petro-derived polymers. Poly(3hydroxybutyrate-co-3-hydroxyvalerate) (PHBV), which is gaining popularity due to its biodegradability, is used in developing blends and composites for a variety of applications. To enhance the miscibility between different components of a material with PHBV, functionalization of the PHBV chain can be done. In this study, grafting of maleic anhydride (MA) onto PHBV was performed using organic peroxide also, called Luperox [2,5-dimethyl-2,5-di(tertbutylperoxy)hexane], as an initiator. The effects of different initiator and MA concentrations on the grafting percentage, gel content, rheology, and thermal properties were evaluated. Additionally, a chain extender (Joncryl ADR 4468) was added during the grafting process to prevent chain scission of PHBV during processing and to promote long-chain branching. Higher initiator concentrations played a significant role in increasing the grafting percentage. Adding the chain extender further enhanced the grafting percentage of the compatibilizers. Compatibilizers with chain extenders increased the grafting percentage by up to 91% compared with their counterparts without chain extenders. Differential scanning calorimetry analysis demonstrated that the melting temperature of the compatibilizers decreased by up to 8 °C with increasing initiator concentration. Furthermore, the thermal stability of maleic anhydride grafted PHBV (MA-g-PHBV) reduced at higher initiator content, likely attributed to the formation of low-molecular-weight species during processing. The maleated PHBV with a chain extender exhibited improved thermal stability, with an increase of up to 6 °C, attributed to an increase in molecular weight because of the chain extender. This can be corroborated by the rheological studies, which showed higher viscosity, particularly for MA-g-PHBV with chain extender. Therefore, this is the first ever scientific study to improve and analyze the grafting percentage of MA-g-PHBV using a combination of chain extender and varying initiator concentrations. This maleated PHBV with a higher grafting percentage will then facilitate the development of composites and blends with improved performance, even at low MA-g-PHBV concentrations.