It would need multiple knocks to unlock all pathways
Knock (PHB, 254) covers this potential interaction of a multiple lock barrier:
If the object has multiple locks, only one of them is unlocked.
As your lock has multiple locks, it could fall into this, but it seems your dungeon is based around this, so I think I'd try and approach it differently.
DM override - homebrew items need homebrew solutions
Of course, this layered lock state isn't quite the same as 'multiple locks', so it remains up to you as the DM to determine how you want it to work. Given that the lock mechanism is part of the dungeon itself, I would likely opt to treat it differently.
Doing so means having some means of narrating how it works and what is expected (or at least a clue of some sort for them to follow.) Developing this should resolve the situation and give the players insight as to what needs to happen.
Heck, you could even have the knock attempt be a trigger for a magic mouth or something that gives them information.