There is a big difference between what will increase the physical weight handling ability (springs, airbags, radical modifications) and how the vehicle is registered, and even more so, what an insurance company will agree to.
Physical modifications to handle more weight. replacement springs (new coils or leaf packs) and helper springs (add a leaf or airbags) will increase how much weight the truck can handle. Heavy duty sway bars will improve handling, but will hurt off road flex, thus off road traction. Frame reinforcements can prevent damage if done right but will increase the risk of frame damage if done wrong (they tend to create bend points where they transition from reinforced to non reinforced) likewise replacement axles will help prevent axel damage when overloaded as will trussing, gusseting, etc. And of course if you are going to be putting THAT much weight on it, you DEFINITELY need to consider FRONT big brakes, and maybe rear (front upgrade is more important than upgrading the rear from drums to disks or adding a big brake kit to the rear as MOST of your braking power comes from the front brakes) There is also the question of what can your drive train handle. Depending on how much of a hill it has to climb, or what the traction is like, an overweight vehicle can easily burn out a transmission. But these change what your vehicle can handle, NOT what it is "legal" for.
It is conceivably possible to convert a F350 into a deuce and a half if you make enough modifications, but if you are planning on exceeding the registered weight class of the vehicle, you might need to talk to the DMV as to whether or not you need to or even can change it's registration to reflect what your modifications can actually handle. DMV are really the only ones who say you can "legally" haul a given weight... but they are also not the final word on the matter.
Then comes the insurance company... That is a contract between you and them. If you exceed your "capacity", they are well within their rights to say you violated the terms of the contract and are on your own. it is a safe bet that if you are at fault in an accident, (or even involved in one that someone else caused), the insurance companies will have someone investigate to determine if they are liable to pay out, and if you had a bunch of stuff, or modifications they did not know about, they can refuse to pay leaving you on the hook for all damages and possibly charged with driving uninsured. That is something you have to work out with your insurance company, and might have to consider switching companies if they will not work with you and your modifications.
All that said... MANY people exceed their weight limits illegally and doing so depends entirely on what the laws are where you are located. For example, I have never been anywhere that I had to get weighed if I had a trailer on my down size pickups or my old full size van. I am not a commercial vehicle, so I am exempt where I play (I would have to look up the rules if I where to go elsewhere. (Example, I CAN tandem tow here without a CDL, but in nearby states I can not do so)
There is also a question of what is safe... for example the pic grubber posted legally has an additional axle, thus changing the weight class of trucks in some states allowing them to haul a larger camper, but that is barely a light utility trailer axle welded to a mounting bracket (probably a receiver hitch) in no way does it make that truck any stronger... I have seen some that are literally just casters on a mounting bar, but by definition it is a "trailer" thus letting the vehicle haul its combined vehicle weight in SOME states instead of the trucks weight. That is where contacting the DMV comes into play, not only in your area, but where you plan to play and all states in between.
