I saw the following example sentence in this link:
If Gina would explain her situation a little better, I think they'd see where she's coming from.
As seen, both the if- and main clauses use the "would + infinite" form and the sentence does not fall into any of the well-known conditional constructions.
Given this observation (and some other ones), I wonder if it would be correct to say that the well-known conditional constructions only show the most common constructions, and other forms can be used too if the context requires.