Korr has a 2X3X4 cage. There are 2 2X2 levels with steps that are 1 grid going up the back. It is set lengthwise, so the door is one end. I use 1" dowels to support the levels. One of the levels has 2 dowels set 2 squares form the end. The top level has 1 dowel, but it is also supported by the grids, so doesn't really need 2. The dowels are zip tied to the level they are supporting and are 1-2" longer than the cage to help provide more support. I think that it is better to have the dowels going across the shortest number or grids. Depending on the layout of the cage, this might be harder to do.
For the door, I have them on the end. The cage is between the couch and the wall in a corner, so the door has to be on the end. If you are putting the door on the front 3 grid side, then I would do a 2X2 door. If you are comfortable with a 1X2 door, then do that.
It might be a good idea to use the connectors along with zip ties. A taller cage does need to be more sturdy. You could put some dowels of other wood pieces along the side going up for some added stability.
I will try to get some pictures of Korr's cage tomorrow, it's getting late and I am tired.
