We actually made a multi-storey bin cage without tubes needed
Here's an old photo of Scamp's bin cage. The tubes in it are just to connect to the rest of her cage and are 100% optional (the bin cage itself is big enough for a syrian anyway).
We put wooden shelves in the middle cage and used toys to help her get between them.
To connect the three bins we lined them up carefully, then got two much smaller storage boxes, cut the bottom out, then cut holes in both the bottom of the bin and the lid of the one below, with these holes the same size as the smaller storage boxes.
To put her cage together we put substrate and toys in the bottom bin, including one below where the hole to the next one will be. Then we put the lid on, then we put the middle bin on there. Then we put the smaller container through the holes in the base and lid, and fill the middle bin as needed, making sure we have a toy on the shelf underneath the entrance to the next bin. Then we put the next lid and bin on, line them up and put the second smaller storage box through the holes. Lastly we fill the top box and put the lid on.
Scamp gets between them by climbing onto the toy, through the smaller container and up into the bin above. She can also climb down really easily too.
Oh and the smaller containers have a lip that holds them in place and stops them falling through the hole we put them through
