Fiber-reinforced polymer (FRP) additive manufacturing has transformed fused filament fabrication (FFF) by manufacturing products with excellent mechanical characteristics. However, the surface finish and dimensional characteristics of printed FRP parts are typically poor due to protruding fibers and the stair-stepping effect. This parametric study examined an in-process combined mechanical plus chemical finishing technique to improve the surface finish of FRPs manufactured through FFF. This process is particularly useful for internal or complex features that cannot be otherwise finished after printing. In this work, a custom-built three-axis machine with printing, machining, and chemical finishing capabilities was used for the experiments. The effect of mechanical finishing on surface characteristics was first quantified using chip load and spindle speed as independent parameters. Following that, chemical treatment was performed on the already machined surface at two pressing depths (PD), which control the normal contact force acting on the surface. The best surface characteristics were observed at a low chip load of 0.007 mm and a moderately high spindle speed of 20,000 rpm. After chemical treatment using a lower PD, a surface roughness reduction was observed (from 8.041 to 4.988 µm). Increased PD led to even lower Ra values (from 4.988 to 3.538 µm) due to the enhanced fiber encapsulation phenomenon. Finally, the dimensional analysis revealed that the final combined finished samples had less than 1%-dimensional error (0.05 mm), which is an order of magnitude less than the typical error in FFF-printed parts (0.5 mm). This study provides means to conduct finishing in an additive manufacturing environment to reduce the time, labor, and cost associated with post-processing.