Titanium alloys, having high hardness value, high chemical affinity, and low thermal conductivity, pose a challenge to the manufacturing industry in obtaining a defect-free fine surface finish. This article presents a novel magnetically assisted externally supplied abrasive-based finishing (MESAF) process for finishing Ti-6Al-4 V alloy at the nanometer roughness level. In this setup, a ferromagnetic brush was formed around the disc-shaped magnet, and a suspension of abrasive particles and distilled water was supplied from an external source into the finishing zone. MESAF addresses the shortcomings of the traditional MAF process, that is, the concentration and replenishment of abrasive particles in the finishing zone. A parametric analysis was performed, and the influence of process parameters on the change in surface roughness and material removal was investigated. Statistical analysis was carried out, and the results showed that among the various factors examined, the working gap and quantity of abrasive particles in suspension were found to be the most critical in influencing changes in surface roughness and material removal, respectively. Furthermore, in addition to analyzing surface roughness, scanning electron microscopy was used to investigate the process of material removal and the nature of abrasion during the finishing process. A comparative analysis of the surface textures generated by the MESAF, conventional MAF, and grinding processes is also presented. The surface obtained by MESAF had random laymarks without any traces of oxide or microchip deposition. Multi-objective optimization was performed considering conflicting objectives, such as changes in surface roughness and material removal, to obtain the optimized sets of parameters. A fuzzy set-based approach is also proposed for higher-level decision making, considering the preferences of manufacturing engineers. Under the optimized set of process parameters, a surface roughness of 0.058 mu m was achieved from the initial 0.718 mu m after 10 min of finishing.