After completing the campaign, you will go into Veteran Mode. The structure of this mode is the same as the campaign, as in you will be given 4 "side missions" and tasked with completing 3 of them in order to advance to a "veteran" mission, which is really just more of the same. Each of the side missions rewards a Supreme Weapon Mod, and there are only 20 in total. 5 weapons X 4 parts each = 20, as noted by the red text at the top of the screen which reads:
Supreme Loot ?/20
They do not repeat as there is literally only one Supreme part for each weapon slot. This makes it way easier than the base game's requirement to have legendary mods on all primary weapons. You may get lucky and get 4 in a row for one weapon, but most likely it will take you several missions to get all 4 parts for 1 weapon. I ended up with 14/20 mods, and had 3 mods on several weapons before I finally found a 4th for any single weapon. I will most likely go back and grind out the other 6 in an attempt to future-proof myself. Just in case. Mileage may vary, but at least there is a direct path. Happy hunting!