The whole process of creating multi-floor maps is not very complicated, however it's quite time-consuming and it's easier if you have basic understanding of how triggers work.
In this guide I will try cover each step in details, so that you'd able to create your first muilti-floor map even if you haven't worked with triggers before.

Credits to IrgenPacer, creator of the first multi-floor map on Workshop.

The v0.33 udate finally made it possible to create multi-floor scenarious (very limited and not flawless, but I'll talk about that later) by adding two new objects: Spawner and DamageArea. Both can be found in "Gameplay" tab in the Editor.

The Spawner can materialise objects out of thin air, we will use it to spawn the second floor.
The DamageArea wipes objects out of existence, and it will be used to delete the first floor.
I will also use the "trigger_lever_invisible" object. It activates a targeted trigger when destroyed. This will be the way to get from the first floor to the second.

Here's how the whole system works: Player approaches staircase and destroys "trigger_lever_invisible". This activates a Trigger that targets DamageArea and Spawners. DamageArea destroys the first floor, Spawners spawn the objects for the second floor. Easy, right?

Let's begin by creating a simple layout, this will be the first floor of our building.


As I said, the most important objects here are Spawner (SPW from now on), DamageArea (DA from now on) and "trigger_lever_invisible" (TLI from now on). Let's place DA somewhere.

Now we have to change some of DA's properties.

• Damage type: delete
  
• Radius: 0.0 (Ctrl + click to enter the value manually)
  
• Physics force push: 0.0 (Ctrl + click to enter the value manually)

Now select DA and target every object on the first floor, including walls and Terrain. Press "Add Target" on the left panel or press "T" on your keyboard to target objects.


Now place a Trigger and TLI. TLI should be placed near the stairs.
Select TLI and add Trigger as a target, then select the Trigger and add DA as a target.

This is what the building is supposed to look like so far.

At this point you should be able to destroy the first floor. Start the map, approach the staicase and interact with TLI. The first floor should dematerialise after you destroy the TLI.

Let's build the second floor. I will create a simple layout once again.

It's time to add Spawner(s). Each SPW imitates one object, so the amout of SPWs should be equal to the amount of objects on the second floor. To copy an object, select SPW, then press "Click to select which entity to clone". Do this for all objects from the second floor, then recreate the second floor with SPWs.
UPD: I found out that there's a "Create spawners from selection" button that makes the whole process A LOT easier and faster. You have to create a separate floor with normal objects, then all you have to do is select all objects and click "Create spawners from selection" on the left panel.
This is what the second floor, cloned using SPWs, looks like on my map.

Select the Trigger from STEP 3 and target every SPW with it.
Now place the second floor on top of the first one and align second floor's outer walls with first floor's walls
This is what the end result looks like.

This method has a number of major and minor issues that limit its usefulness. Some of them can probably be fixed by the devs, but I'm not sure if this is worth their time.

• Dropped weapons duplicate after floor changes
  
• Discovered area stays after floor changes
  
• Doesn't work properly with more than one controllable soldier. Can't move soldiers upstairs one by one. They stay in their places after the floor changes
  Two solutions:
  1. Have only one soldier on map
  2. If you want to have more than one operator on map: use DA to kill soldiers that aren't close enough to stairs
  
• Game freezes in certain conditions when going upstairs
  
• Instead of moving (teleporting) to the other end of staircase, soldiers stay in one place
  Two solutions:
  1. Use elevator instead of stairs as a way to change floors
  2. Delete the soldier and spawn another one after floor changes