“Silent teleport” is a original Doom trick often used to good effect - Doom isn’t true 3D, but one floor ‘above’ another can be achieved by invisibly jumping between areas horizontally displaced in the underlying map.
Vertical, floor-to-ceiling portals are a bit more new. I think only the Eternity Engine and GZDoom support those. They also support portals that render the other side, monsters and everything.
Edit: Oh, I forgot that you can get portal-like behavior in the Vanilla engine by hacking the BSP tree used for rendering, see https://doomwiki.org/wiki/Linguortal and also here for a more visual demonstration: https://www.doomworld.com/vb/thread/74354
If I recall correctly, the only way Doom (the game) achieved dissecting planes was to have stepping stones.