Wanted to throw something into the mix here. I added a third Tier IV materia onto 2 items in a row on the day of my in game birthday. Whilst it could have just been pure luck, both synths were at around 8% chance of success so it would be pretty damn rare to do that twice in a row so maybe it was some kind of birthday present? lol
I would not be surprised if there were some kind of hidden modifiers in game but there is not a chance in hell that the Devs are gonna share the secrets. They play the game too so they would never be able to sell all their triple melded gear up on the wards right now if they shared the secrets with the masses!!