I dont think this is a battle you want to take on. It will require a structural engineer to design, a certified welder to build it, and then someone is going to have to test it. It will probably be easier on the wallet to buy a new box. I say this because if something happens with the box where someone gets hurt, the lawyer is going to go after the trench box company first. When the trench box company sees what was added to the box, they are going to say, not us, we didnt add that on, then its you whos on the hook.
That being said, something ive seen done in bad ground is to weld a plate on the back of the box. It would keep anything the collapses around the back of the box out. Not sure how much it will help you though