John, this is not a good idea. To begin with, you will add a lot of weight for the structure and then have a lot more weight added with wind loading and possibly snow loading. Not if but when the roof blows off, your neighbors and their insurance companies will enjoy suing you as they will get everything fixed that was ever wrong with their places.
Your insurance company will not be happy with this possibility, and the police might not be either if your roof happens to land on the Wicked Witch of the West.
Your trailer was designed for a particular roof load and the walls were designed for the weight. Ever seen anybody crush a pop can? The results will be similar though it could take a lot longer than the one hit that works best on a pop can. Probably one result that will start pretty quickly will be leaky walls.
I'm sure that you would never be tempted to take this on the road again, but it sure congers up an image that fits C. W. McCall's Wolf Creek Pass song. Consider what would happen to a truckload of chickens if you tried to go under a bridge that went up to the 12 foot line and the chickens were stacked to 13'9. LOL
Or you could put the roof on and sell tickets to watch it when you tried this. Might be able to make enough to buy what you really want.