Multi-room trap?

Theoretically, how could a multi-room trap work in DND? I'm running a noncombat mini dungeon, and think a multi-room, complex trap would be neat, and easier than making a puzzle, but I don't have the first idea how I would start or how it would work

It all hinges on what you want it to achieve. 

What do you want to happen in the final room?  What do you want to happen to the party?

Is there any possibility of avoiding the trap?  If not, I would recommend it might not be the best idea.  If so, how?  And, perhaps more importantly, how will you signpost that they are walking into a trap and how will you signpost how to avoid it?  Is it timed?  Is it set by certain actions?  Is it avoided by certain actions?

I would need to know a little more of your intentions before I could give you any more concrete ideas.

The final room is a boss fight, that's why I don't want combat in the previous rooms.

There is a way to avoid it, and an observant player will notice/know that you probably shouldn't take treasure from an abandoned dwarven forge.

They're with an npc who's secretly tryna kill them, so I don't think an obvious signpost would be great, but maybe there's a warning plaque

I mean, you'd always be better off not touching anything but where's the fun in that (or the profit)?

This will not be easier than a puzzle, in all honesty it's going to be a puzzle.  And I'm sorry, it will be easier for you if you use a flow chart.

Disclaimer - these are my (very quick) thoughts and only mine-

Your end goal is to get them to the big bad, perhaps that fight will be harder or easier depending on what they do in the preceding rooms - that could be something happening in the antechamber that gives them a disadvantage in the big boss fight or an advantage in the room with the big boss.

Ideally, you want to work backwards through the rooms, this way you can signpost the wrong thing to do - they should have a view of the final room with any good things being visible - rising columns to give you advantage (ancient prison bars), rising rocks to give you cover (guard nooks).  Maybe this was a chamber to keep the big bad imprisoned - so some sort of magical item that saps its strength that can be lowered from the ceiling (it got deactivated and rose up - that's what allowed him to escape).  It's empty for now so they can have a look around - the bad guy is upstairs. 

Have the party hear some frightened chatter from the tunnel ahead - there's another party here.  They have been wondering through the 6 rooms and, idiots that they are, have been robbing everything they can get their hands on and touching everything they shouldn't.  Your party hears screams, thuds and a final, desperate cry for help.

Would your party go into the tunnel?  You will need to think if they'd be tempted or not.  Perhaps a sudden strange howl behind them would help them. Perhaps they hear their footsteps sound as if on a hollow floor as they find the rooms.

Anyway, from there let them move through the rooms.  Perhaps 1 room is simple - they see some cogs, an adventurers hands on a wheel - he's been electrocuted.  Maybe you combine 2 rooms - they find a large crystal similar to a crystal from another room... on closer inspection they find tiny boots and armour crushed under it.

I think it could be fun.  You'd need to think a little longer on it but I hope it gave you some ideas.

Sorry if I missed your point.