> But also, what you describe would be incorrect, since two <MAX values can add to a value that is >MAX, and overflow

I was maybe unclear. I meant, if you know a sum can introduce overflow (because you have a check right after), why not check the inputs before doing the sum, instead of checking the sum?

You can do something like

       (y > 0 && x > INT_MAX - y) 
    || (y < 0 && x < INT_MIN - y)

    ((x ^ s) & (y ^ s)) < 0