Just a question as to tire weight rating vs vehicle capacity. On my 2016 Expedition EL with H-D Trailer Towing Package, would tires rated at 113H match up with the total rated load for this truck? I believe that rating is 2554 pounds. My terminology may be off. According the Pirelli's site and the sidewall, to get max load, I would need to run at 51 pounds, which helped a lot on the initial tow of my new travel trailer.
My tires are 275/55/r20 113H Pirelli Scorpion Verde - which were a great update from the stock tires.
Also, when towing with a weight distribution hitch, would I need all four tires at that pressure as opposed to just the back. I am thinking just the back as that is what is holding the tongue weight.

 

Looks like stock tires have a load rating of either 111 or 113 depending on the brand tire, or maybe the towing package gets 113. H is a speed rating and is better than T, topping out at 130 mph(H) instead of 118(T). So you're fine with 113. I'd increase pressure in all 4 tires to keep the truck balanced when unloaded, and I would not go more than 5-8 lbs over the door jamb sticker pressure label.

 

I know this is a bit different than what you were originally asking. I found that the best thing I ever did for my overall towing experience next to getting a good WDH, was switching over to LT tires vs the regular P tires. It was more than just night and day in terms of the overall handling of my Expedition towing our travel trailer, the Expy finally felt planted firmly on the road. This also helped immensely when it was windy out as the Expy was a lot more stable with the LT tires. It did make the ride a bit more firm over bumps, but it was nothing that bothered my wife or myself and even she like how much better it felt driving through curves, turning corners, etc. The LT tires can also handle a lot more weight and air pressure. We run ours at 35 psi when we are not towing and bump them up to 60 when towing as per what the manufacturer told us we should be running at for the tires we had with the weights we had on each axle.

Yes I would have all four tires running at the same PSI when towing.

 

I wish I had gone with LT tires, but since I just replaced them a few months ago can't really pay for that upgrade at the moment - unless I had those moved to my pickup (2018 F150 ) and got new tires for the expedition. Might be an idea.
Just realized that won't work as truck comes with 265/60/r18.

 

Door jamb, if I recall correctly, shows 35 PSI on the stock tires. But with tire rated at 51, I would think I could get closer to that level (albeit bumpy and harsh when not loaded). I had brought the rear to 48 last night and front to 40. Might revisit that approach.

 

Remember the psi rating is the max for the tire and will carry the rated weight safely at that pressure. you can run any pressure that works below that max rating, a lt tire will need less psi unloaded to keep the tread even on the road for even wear and longest tread life. running a higher psi unloaded will wear the center 1/3 of the tread faster and you get less safe miles out of the tire. An old trick taught to me by a tire guy long ago was to make a good solid mark side to side on the tread and then drive a ways and look at how your mark is wearing off, if the center is wearing off faster than the edges then you have it over inflated. If the edges are wearing faster than the center then it's under inflated. You can make air adjustments and remark until it's even. Takes some fiddling to get it right but I've had great luck over the years with a lumber crayon and a little time to get even wear on all 4 tires. I usually do 1 front and 1 rear every time I change tire or wheels to get a baseline, then that's my unloaded psi for the life of that combo. currently I'm running D load range Coopers on the Expy and 31 psi is just right and rides like stock. It's not extremally precise but I always get good tread life from using this trick. When loaded and towing I would run all 4 the same, remember that your weight distributing hitch's function is to distribute some of the load to the front suspension and help keep vehicle level and stable. With WD hitch set up correctly the front and rear will be sharing the extra load close to evenly so it will handle better with all 4 at an appropriate psi. Jim

 

That was my understanding or expectation as to the purpose of the max pressure on the sidewall. I was humored by Pirelli's lawyerfied response - we recommend using the tire pressure specified on your vehicles placard.
I realized the weight distribution hitch essentially tries to make the trailer and tow vehicle "one" in terms of a structure and distributing the load. In the past I have not been as close to limits and more than ample towing capabilities for my travel trailers. With the latest acquisition I am getting a lot closer to limits. I suspect my hitch is not fine tuned, but will know more Friday and Sunday going to and come from a state park near Bastrop, TX, about a 2.5 hour drive. I went ahead an bumped up pressures to 48 all the way around. Rides a might stiff without the trailer.