Here's some fun stuff from J.D. Denniston's Greek Particles (amazon.com). These are from the introduction so they are necessarily generic.
The different methods of connexion.These are, broadly speaking, four: (a) Additional, (b) Adversative, (c) Confimratory, (d) Inferential. But the divisions are everywhere fluid. (Denniston, Intro, xlvii)
...
(b) Adversatives are of two kinds: eliminative adversatives, used often where on of two contrasted members is negative, the true being substituted for the false (par excellence μεν ουν and normally αλλα), and balancing adversatives, where two truths of divergent tendency are presented (δε, μην, μεντοι, etc.) (Denniston, Intro, xlix, bold mine)
Note that "eliminative" and "balancing" are Denniston's way of saying "strong" and "weak" adversatives, respectively. Then, the money quote (for my purposes):
(7) Abnormalities of reference in connexion. The connexion established is, normally, of course, between consecutive units of speech: words, phrases, clauses, or sentences. There are, however, certain exceptions. In dialogue, owing to the quickness of thrust and parry, or the self-absorption of one of the participants, a speaker sometimes links the opening of his speech to his own preceding words, not to the intervening words of the other person. ... In S.El.1035 (p. 443) αλλΚΌ ουν looks back to 1017-26: or perhaps it would be truer to say that its point d'appui is the general situation, the whole attitude of Chrysothemis, rather than any particular set of words, an explanation which applies also to E.Alc.713 (και μην, p. 354), and IT 637 (μεντοι, p. 405). (Denniston, Intro, l, bold mine)
The page references are references to further discussion within Denniston. So, p. 443 gives us the context of the citation that Denniston mentions:
1035 ('Well, since you refuse to help me (1017-26), do at least realize what that refusal means'). (Denniston, 443)
So Denniston supports the idea that αλλα can provide a link between discontinuous text; or that the adversative/contrast/whatever you want to call it can be a response to a general idea floating in the ether (the "general situation", as Denniston calls it). Both of which support contentions I previously posted on in The αλλα Funnel.