Room over room (as done in later build games) usually does not require the sectors to overlap in this manner as it is a different thing (it is extension of how swimable water works, where the engine renders the other sector instead of floor/ceiling).
While Lunatic Fringe is pretty in-your-face example of impossible geometry in build, the duke3d maps contain many more cases of intersecting geometry. Obviously such things are impossible in Doom because there is no way to build BSP tree out of that and because doom only tracks X/Y coordinates of player(s)/monsters.
Modern source ports are a totally different thing. If any, try to do what the former comment states
with a Boom compatible engine as Crispy Doom or Chocolate Doom.
The portals in prey were cool but, definitely the games Portal and Portal 2 are places you could see it elsewhere. Also in portal you can actually choose where the portals are, whereas Prey's portals were fixed in place
Is there no way of building a BSP out of it? I don't see why it has to be Euclidean to be partitioned, and loops are also possible (e.g. Deimos Lab). (The coordinates are definitely a blocker, so this question is academic.)
The “sectors” in the resulting level data have to be convex for the doom engine. The “asset pipeline” handles that by breaking up non-convex geometry into smaller convex sectors. So, there are no loops or holes in the actual level data, also from the cursory glance both of the large loops in Deimos Lab are actually not complete loops, but they have a place where the loop is broken. But that does not matter that much, as almost any level contains geometry that is either concave or has a hole (courtyard in E1M1, both large rooms in MAP01…)
The Doom design starts with X,Y,Z and then finds your BSP node. You can't warp to a different X,Y,Z without some type of warp portal which doesn't exist in Doom. Modern Doom forks have this feature and also have graphics portals so you can implement this (as MyHouse.pk3 does).
I meant that as in contrast to build tracking the sector the thing is in. Due to that you can have two sectors that intersect not only in 2D, but even in 3D and the engine still does the right thing (ignoring the fact that the renderer gets slightly confused when there are overlapping sectors in the view)
The primary thing that BSP does is that it maps coordinates onto a BSP node/sector. Thus you cannot have overlapping geometry, as this mapping would not be unique. Quake has some idea of portals (I'm not sure about Doom), but it is used only as an additional layer of optimization, the engine is not fundamentally portal-based.
While Lunatic Fringe is pretty in-your-face example of impossible geometry in build, the duke3d maps contain many more cases of intersecting geometry. Obviously such things are impossible in Doom because there is no way to build BSP tree out of that and because doom only tracks X/Y coordinates of player(s)/monsters.