2 deck boxes
Here's a story:
Alex arrives at a tournament with his deck, but is unsure what the exact 60 cards will be. He's deciding what the last 2 cards will be. He even has all the cards sleeved, so he can test out the different versions. After writing out the decklist, he changes his mind about what to play. He crosses out the 2 cards and writes in the other cards. Now he has to decide what to do with the extra cards. He remembers that judges have told him that he cannot keep those cards with his sideboard, so he puts them in his other deckbox (one with only dice and tokens).
Now, is there a different story, where Alex has the cards in the other deckbox, so that he can have 2 sideboards and hope that his opponents don't notice him taking cards out of both deckboxes? Sure.
If Alex is deckchecked, hopefully the judges will ask Alex some questions and try to determine if story #1 or story #2 is true (or maybe some other version). If story #1 is true, then there is no infraction. If story #2 is true, then they are cheating. As Emilien started, these are elements in your investigation.
As judges, we are constantly telling players that they cannot keep other cards with their sideboard. Please do not start penalizing players with Deck Problem infractions, when they are doing exactly what we have told them to do.
Shawn