Only a true Texan can tell you the difference between "y'all" and "all y'all".
But if you're referring to a set of birds and fish together, then the usage is "all y'all" because the canonical partition yields more than one subset (one containing birds, and one containing fish). The distinction helps differentiate between whether you mean the superset or one of those subsets.
It works with any other partition which might be obvious (not just birds and fish). If you have two families together, you might avoid "see y'all later" because it could be interpreted that you only expect to see one family later. "see all y'all later", by contrast is unabiguous--you mean both families.
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Did I get it right? Am I a true Texan?
There's another usage that comes to mind, though. One might argue that "y'all" borders on a second person plural inclusive of the speaker whereas "all y'all" marks a distinction between the speaker and the others. For instance, a peeved person would be more likely to say, "All y'all can kiss my ass," as opposed to, "Y'all can kiss my ass." "Y'all" by itself is more friendly and self-inclusive than "all y'all", which carries an inherent otherness to it.
I'm under the impression that the double negative is a relatively modern thing (early 1800's). Previously, repetition of the negative just reinforced it, like:
> I ain't never put syrup on my bacon on purpose
...just double-enphasized the negative, rather than letting the second negative negate the first. This feels similar except instead of stacking negations you're stacking separations.
So a first person plural?
Grammatical constructs can have a lot of variation between languages, and there are certainly nuances that can't be expressed in English the same way that it can be in other languages. One thing we lack is a nuanced sense of past, while other languages have baked in ways to express recent past or distant past (e.g. Bantu languages).
My proposed interpretation regarding "all y'all" is not academic, just a native feel, and I'm sure other native speakers could disagree.
Y’all can kiss my ass; ladies and polite company excluded of course.
All y’all can kiss my ass.
All y'all need to come to my BBQ tomorrow. I can't eat 50 pounds of brisket by myself.
Y'all is plural. All y'all is short for all of y'all.
still, brilliant nonetheless.