The mechanical performance of parts produced by fused filament fabrication (FFF) has been limited due to the presence of voids and poor interlayer welding. Recent advancements in FFF have enabled the fabrication of void‐free objects with strong interlayer welding through the use of semicrystalline polymer shells such as high‐density polyethylene (HDPE) along with a high viscosity core polymer like acrylonitrile‐butadiene‐styrene (ABS). The zero‐shear viscosity (η0) of ABS is three orders of magnitude higher than HDPE making the ABS‐HDPE core‐shell configuration preferable. ABS holds the shape by preventing bulk flow and part bending while HDPE promotes full surface contact across the layers. Most polymers, however, are immiscible which causes a weak weld line along the core‐shell interface. Herein, maleic anhydride (MAH) is grafted to the butadiene segment of the ABS core thereby compatibilizing the interface with HDPE, improving the interfacial adhesion. Attenuated total reflectance‐Fourier transform infrared spectroscopy was employed to confirm successful grafting. Using a custom‐made die affording the core‐shell structure, the ABS‐g‐MAH is shown to improve the impact resistance by 253% and 16% compared to neat HDPE and ABS specimens, respectively. Additionally, a 10% increase compared to the unmodified ABS‐HDPE core‐shell configuration is observed.