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I think there's "extremely effective" but I'm not sure if I've only seen that in fan-made games. Also in what games are they and how far does it go? I'll take WIP answers this is pretty much relevant to most Pokémon games.

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"Type is the type effectiveness. This can be 0 (ineffective); 0.25, 0.5 (not very effective); 1 (normally effective); 2, or 4 (super effective), depending on both the move's and target's types."
Not going to use this as an answer, but I don't know why Bulbapedia would list both 2x and 4x as super effective, so I'm assuming it's super effective when it's 4x as well.
https://bulbapedia.bulbagarden.net/wiki/Damage#Damage_calculation
I honestly feel like it would be so cool if it went as high as it theoretically can, would add another element of luck and rarity to the game. btw I know it's "super effective" for x4 too, it says it in most if not all games.

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As of Gen 8, official games do not. I Iron Headed a Carbink just yesterday with my Excadrill (4x weakness to Steel), and still only got the standard "super effective". Though I love the idea of differentiating text for 1/4 and 4x matchups.

As for fan-makes there are too many for the average person to test, and they're forbidden from discussion here anyway.

I'm not sure what you mean by a "WIP" answer, but I hope I helped. If not, let me know specifically what you're trying to cover and I'll see if I can edit.

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Because my memory of something like that is almost 100% from one of the more popular leaf green rom hacks, but I was asking about official games and if GF do something once they usually continue the trend, thanks.
So if someone was to check every bootleg pokemon game in existence for whatever reason, they wouldn't be able to finish this century.