The capacity to tow is the lesser of the hitch rating or what's left in the GCWR of the MH after doing the math of GCWR less the weight of the MH how it's loaded for travel. Simply adding a hitch of 5000 if the MH can only handle 4200 won't get you anywhere. You have to load the MH for travel, weigh it, do the math and then see what - if any - capacity you have left. THAT is what you can safely tow. You may find it's well short of the 4200.
But you are starting off knowing you are already overweight without a drop of water, food, fuel or people with the toad you have. So it's a moot point. You need a smaller TOAD or a MH with more capacity.
You can't just add a hitch and expect the MH's capacity to increase like magic, there are constraints on the chassis, drivetrain, brakes etc that engineers use to calculate the capacity to start with. Adding a hitch doesn't change any of that. If I am not mistaken, FR adds the frame members to the MB chassis and rates it at 4200 lbs. So unless you are going to beef up the frame members on the chassis at a minimum, adding a 20k hitch does nothing and still leaves you with 4200 to tow and a pack of crackers in the mh.