towing capacity upgrades?

I have an 06 explorer 4.0L XLT and am trying to boost the towing capacity. From what I've been reading swapping gears doesn't seem like the way to go, but a trans cooler and a brake controller should help. I already have the class 3 receiver and wiring. Is there anything else I should consider? Anyway I can safely get some more power out of the engine?

 

[thebrakeman]

If the class 3 hitch (2" square receiver) and 7-pin wiring came from the factory, then you already have about 5500 lbs max tow rating, and should not go any higher.

If you added the class 3 hitch and wiring yourself (stock hitch was 1¼" class 2), then you are stuck at 3500 lbs max unless you upgrade the gearing and cooling. 4.0L V6 Explorer without the towing package has a strong enough frame for more, but the drivetrain is lacking.