Arthur Lannister asked:

I don't think so. Besides I'm not sure if removing more than 12 chains is a good thing.

You could get super-technical about this and say that when executing the Mulligan rule, you aren't really "shuffling your deck," the same way that playing a dupe is not really playing a character or an attachment (because you are executing the duplication rule). You could also argue that the Mulligan rule talks about "re-shuffling" your setup hand into your deck, arguing that the shuffle you do when you take a Mulligan is a sort of "continuation" of the original one.

But all that is splitting hairs and playing with technicalities. The better precedent to follow would be the Defenders of the North Agenda, which had a Response for "after you draw cards during the draw phase." It was ruled (and might even be in the Legacy FAQ...) to only apply to the standard framework draw, not to any other permissive, optional draw effect you might get through a card effect. Same sort of thing happens with Kings of Summer; no one tries to apply "draw 1 additional card during the Draw phase" to every draw effect that might be triggered in the Draw phase - just to the framework draw. Following this precedent makes it seem likely that the proper way to interpret the Maester Agenda is that it only refers to the shuffle you must do from the rules, not to the shuffle you might do - if you choose to take a mulligan.

Ultimately, I think Rogue30 is correct: pulling a total of 24 chains out of your deck with a Mulligan shuffle is not a good idea. Needing to win 24 challenges with a Maester on the board (assuming all the chain attachments are "Maester only") is a pretty high hurdle. (The real benefit would be to pull two copies of your favorite chain out and onto the Agenda, not using a technicality to thin your deck.)

Play 24 chains out of my deck ? who would do such a stupid thing ?

Just a question asked on french board. We are people that love puzzles I guess, so thank you guys for detailed explanation.