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Twins is a 1988 comedy featuring Arnold Schwarzenegger and Danny DeVito as genetically engineered twins. The fact that they’re genetically engineered is used to explain the differences between Arnold and Danny, but the movie would’ve probably worked as well if they would’ve been regular brothers.
If they would have been is something I would never say. In my dialect, if they had been is the correct choice. And I don’t think I’ve ever heard the if they would’ve been construction from anyone here in the middle of Ireland, or even from anyone on this side of the Atlantic, but it is certainly common online.
I suspect that this is currently a purely American phenomenon, but I could well be wrong about that.
I am not sure what search terms to use to do my own research. The phrase “double conditional” is one I came up with as I asked this question. I’m certain it’s not the standard term used to describe this usage. And most results from a search are about programming languages. However, I did turn up a couple of relevant references.
DEAR GRAMMAR LADY: A prominent scholar made the following statement in a recent article. “If we would regard religion as a work of art — as a piece of music — we would have a different understanding of it.” The “would” in the first clause strikes me as being incorrect usage/phraseology; i.e., I had expected “If we regarded or if we were to regard.” (sic) Could it be that even scholars of great renown are capable of such blatant mistakes?
ANSWER: You are correct. She is guilty of what I call the “double conditional.”
Mary Newton Bruder, The Grammar Lady, Pittsburgh Post-Gazette, April 7, 2000.
I also found one discussion on an English-language forum, but it goes off topic almost immediately.