My understanding is that this situation is covered by the "Can Parts be Replayed?" question in the current FAQ: "A group of characters that play only part of a chapter or adventure can't return to that chapeter unless the entire group agrees to do so." The next sentence clarifies that "the entire group" includes the DM.
However, as noted in a different thread, it's not clear if "the entire group" means the entire group finishing the previous session, or the entire group about to start the new session. The example suggests that "the entire group" is meant to apply to the group ending a previous session, but this suggests that new players wouldn't be able to join a group in progress, only after that group reaches the end of a chapter.
So, borrowing Jasper's example above:
- Jasper finishes running the Hill Giant Steading section of Storm King's Thunder, and Pauper is going to start running the Frost Giant Jarl section of the same adventure (which is in a different chapter, IIRC) at the next session.
The 'parts being replayed' rule doesn't apply here, as you're moving from one chapter to another -- no problems I can see.
- Jasper and Pauper are both running the Hill Giant Steading portion of Storm King's Thunder, and some players want to move from Jasper's to Pauper's table after a given session.
A strict reading of the 'parts being replayed' rule would prevent this.
- Jasper and Pauper are both running the Hill Giant Steading portion of Storm King's Thunder. Jasper, however, is taking a break from DMing because of other commitments. Some of Jasper's players want to move to Pauper's table to continue playing Storm King's Thunder.
Again, a strict reading of the 'parts being replayed' rule would prevent this. However, to avoid having to turn players away from the game, the local organizer could authorize additional players to join Pauper's table, if there is room (the maximum table size remains 7 players, regardless of whether the adventure is a DD-series adventure or hardcover) and if the existing players agree. In general, the Adventurers League admins are in favor of running games over not running games, though the games should be legal AL games.
- Jasper and Pauper are both running the Hill Giant Steading section of Storm King's Thunder, and Jasper's table is slightly ahead of Pauper's table. Jasper's players play through a massive battle with a powerful magic item reward, but a few players, disappointed that they didn't get the magic item, decide to move to Pauper's table the following week to replay the encounter and give themselves a shot to get the item.
This is flat-out not allowed by AL rules -- "Replaying the entirety of a portion of an adventure you want to replay is not permitted." (FAQ v7.1, p.13)
Hope this helps clarify things!
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Pauper