Ok, here's what I would do. First, zip tie the current top level grids together, if they aren't already and remove the connectors at the top. Buy either a 1-1/4" wooden dowel, or 2" x 2" piece of lumber long enough to run the length of the cage (roughly 58"). Run the dowel or 2" x 2" thru the grid in the top corner of one of the panels (in the center of the cage). Like the one supporting the roof in the picture...
You may need to sand or cut the ends a bit to make them narrower so they fit in the holes easier. I had a heck of a time! Then build the upper level. Hope the picture is a help. My explanation, maybe not-so-much?! :-)