What specifically do you want to tow, this will determine how drastic the mods need to be.

 

There is nothing you can do to legally change the towing capacity of your truck (since you brought up legalities). As such, no matter what modifications you do to the truck, it will still legally have the same capacity and if something happens and things are probed into, your liability could be huge if you knowingly tow beyond your capacity.

Now, as to the question of what can you do to increase towing capacity and not kill everyone on the freeway, you need to explain what you're trying to tow, what the limits of your truck are (see door jamb stickers, although I don't know if a 2006 has a yellow payload sticker, as well as the sticker on your hitch (lay down and look up) if it is still readable). Your hitch has a capacity without a weight distribution hitch, and a higher capacity with a wdh. The truck axles have capacities - GAWR, as does the overall truck - GVWR.

Changing the gearing makes nothing safer, it merely impacts your ability to come to speed with a heavy load.

 

Depends on your definition of "towing capacity". If you don't already have it, you can increase the towing capacity as defined by Ford by simply replacing the ring gear and pinion in your rear end with a 3.73 ratio. Assuming you have a SuperCrew shorty 4x4 with 3.55 axle, your tow rating is 8,200 pounds. Replacing the 3.55 with a 3.73 ring gear and pinion will increase that to 9,200 pounds. I hope you don't want to tow a trailer that grosses more than 9,200 pounds with your F-150, so if you have the 5.4L engine, towing capacity is not your problem.

The tow rating indicates the max weight your drivetrain can PULL without being the slowpoke holding up traffic on hills and passes. But it ignores payload capacity. So in the real world, Ford's tow rating is significantly overstated. It assumes a truck with no options not required to obtain that tow rating, and with no weight in the truck but a skinny driver. The actual limiter as to how much trailer you can tow without being overloaded is the payload capacity available for hitch weight. Payload capacity available for hitch weight is the GVWR of the truck minus the wet and loaded weight of the truck. There is no reasonable way to increase the GVWR of the truck.

So the way to increase the max trailer weight of any trailer you can tow without being overloaded is to reduce the weight, including hitch weight, of the wet and loaded F-150. Hitch weight is part of the wet and loaded weight of the F-150, so hitch weight is your problem.

How to reduce hitch weight? You must maintain about 12% to 13% of trailer weight of a travel trailer on the ball for decent towing stability, so there's not much you an do to reduce trailer tongue weight other than tow a lighter-weight trailer. So you're up stinky creak without a paddle?

No. There is a solution, but it's not cheap. It's called a Trailer Toad. It's sort of a dolly that puts most of the hitch weight on the wheels of the dolly instead of on the ball of the hitch, so it adds minimum hitch weight on the tow vehicle. With a Trailer Toad you can use all the tow rating for trailer weight and not need to worry about payload capacity. There is more than one brand of dolly that is similar to a Trailer Toad, but here is a link to the real McCoy:
http://www.trailertoad.com/index.html