I've written before (and also hold this in my paper for the upcoming ETS meeting) that αλλα is a marker of contrast. This means that when one runs across an αλλα, the first thing that one should do is determine the items being contrasted. You'll likely miss the import of the passage and the structure if you don't do this.
In most cases this is easy. Here's an example from 1Cl 4.13, the Greek and English are that of Lake:
13 διὰ ζῆλος Δαυεὶδ φθόνον ἔσχεν
οὐ μόνον ὑπὸ τῶν ἀλλοφύλων,
ἀλλὰ καὶ ὑπὸ Σαοὺλ βασιλέως Ἰσραὴλ ἐδιώχθη·.
13 Through jealousy David incurred envy
not only from strangers,
but suffered persecution even from Saul, King of Israel.
This is a pretty standard "not only ... but also" / οὐ μόνον .. ἀλλὰ καὶ construction. It happens in the NT frequently. The idea here is that David may very well have expected to incur envy from strangers, but Clement says that even Saul was jealous of him to the point of persecuting him. The contrast is between the 'strangers' and Saul. Most examples of αλλα are like this. Particularly when a negator is used, the items being contrasted are fairly easy to find.
But then, right after this verse, we come to 1Cl 5.1. A chapter that actually starts with αλλα. So what is being contrasted?
1 Ἀλλ ̓ ἵνα τῶν ἀρχαίων ὑποδειγμάτων παυσώμεθα, ἔλθωμεν ἐπὶ τοὺς ἔγγιστα γενομένους ἀθλητάς· λάβωμεν τῆς γενεᾶς ἡμῶν τὰ γενναῖα ὑποδείγματα.
1 But, to cease from the examples of old time, let us come to those who contended in the days nearest to us; let us take the noble examples of our own generation.
Chapter 4 of First Clement is a laundry list of OT personages, listing examples of jealousy (such as that described in 4.13 above). Chapter 5 switches the focus from examples of the past to examples of the present. The balance of chapter 5 speaks of "pillars of the church" and gives further examples of Paul and Peter.
This example of αλλα is interesting because the contrasted items are at the paragraph level and perhaps might even be said to be at a higher level. But most, if they were classifying this instance of αλλα, would call it transitional because it seems to transition the discourse to a different topic. And that's true, it does. However, this isn't a different use or sense of αλλα; it is simply αλλα doing what it does at a higher level in the discourse; instead of functioning as a conjoiner of phrases or clauses, this instance joins (depending on how you view it) paragraphs or clause complexes and clues us in that these higher-level discourse items are being contrasted.
Denniston (The Greek Particles (amazon.com)) notes this sort of usage, but it is hard to find in grammars that focus specifically on the Greek of the New Testament era.
Yet another reason why reading Greek, and reading Greek from outside of the NT but still in the same general era can be an enlightening exercise.