Can the first secondary of a green mod increase more then once?

From my understanding: at levels 3, 6 ,9, & 12 a secondary stat is added. If the mod already has all four secondary stats at one of these points, then it will instead get an upgrade to a random existing one. So a green mod will only get one upgrade to a secondary stat because at each of the other 3 upgrade points it is instead adding a new stat.

3, 6, 9, 12 all add a secondary stat. If the scheduled add is already present, the increase is given to an existing stat. Don't have to fill it with all four to get a bonus. In this case, it means that the secondary stat showing on a green will be the one to boost.