pothos.org

The Amphictyonic League met at Thermopylae and Delphi on the spring and autumnal equinoxes respectively. Philip had received two votes of the Amphictyonic League in 346. Yet he instituted a separate Hellenic League (now called the "League of Corinth") in September 338.

Demosthenes had been agitating against Macedon and encouraging many members of the League of Corinth to ally themselves against Macedon prior to Philip's death in August 336. Diodorus, History, 17.3.2 & Plutarch, Demosthenes, 23.

Alexander called a meeting of ambassadors in Corinth in winter 336 AFTER he had met in Thermopylae about September 336 to be approved as head of Amphictyonic council. Diodorus, 17.4.9 & Justin 11.2.

Did the "League of Corinth" replace or supplement the Amphictyonic League?

I really don't know, but it is my understanding that an amphictyonic league was a confederation of cities to protect a temple and its treasures. The Amphictyonic League was concerned with Delphi, but maybe the League of Corinth grew out of it to show a change in leadership, a change in venue and a change in purpose in being concerned more with sacred vengeance against the Persians. Just guessing though as I don't have the resources to do this sort of research.

The koine eirene of Philip II was quite a different thing compared to the Amphyktions ("dwellers about"). The latter was a more "localised" affair and, in the end, a tool to be used for Philip's intervention in central Greece. The former was a political structure aimed at control of Greece with Philip (Macedon) as its undisputed hegemon or prostatai. Symmachia (alliance) was also a part of this which set it apart from earlier versions of the "common peace".

Enough on this phone - no matter how smart it reckons it is!