I built melamine cages several years ago. I went with a very simple bookshelf design. The shelves were cut from one 4’x8’ melamine sheet (Home Depot made the cross cuts for me). The sides were two 4’ melamine shelf boards (no cuts needed), and the back was made of a sheet of backsplash board (about 1/8” thick with one side glossy, also cut by Home Depot). I predrilled through the sides into the shelves and sunk three 3” screws into each side of each shelf, and 1/2”-3/4” screws to attach the backboard - also predrilled. By the time the shelves and backboard were secured, there was no need for additional bracing.
I used plexi doors in aluminum tracks, but if I did this again I’d used hinged doors with a litter dam. I used silicone to seal the cages and mounted Ultratherm heat panels on one end as I just needed to create a warm end in the mid-upper 80’s. With balls or boas, I’d use radiant heat panels on thermostats. To make it easier to move, I added heavy duty casters to the bottom. The casters were mounted to 1”x4” boards that spanned the width of the bottom cage on each end, which were then mounted to the melamine. This was to ensure that the melamine didn’t crack or break from the weight of the cage on the casters as it was rolled. As said by others, melamine is heavy...the casters helped, but they need to be industrial strength.
As the cage ages, you will have to reseal as scraping urates and cleaning take its toll on the sealant. Once liquid gets into the melamine through failed sealant, the melamine will begin to separate...and you cannot get rid of the odor if the liquid that gets absorbed is urine. I used these for a few years, but eventually upgraded to all plastic caging with radiant heat panels. They are much, much lighter and easier to clean, disinfect, and deodorize.