I should also add, I am a three axle, six tire trailer....with a 20k max weight...right now we are 18.5k, give or take with holding tanks.
I'm guessing the 20k lb tri axle trailer has 6k axles which the Michelin XPS Ribs or the Bridgestone R-250 both being a all steel ply carcass commercial grade LT tire would be a best choice on that big tri axle.
There are also some lower priced very good fabric ply LT E tires @ 3042 lb capacity.
If the trailer has 7k axle then the Goodyear G614 RST or the Sailun S637 both being a load range G tire at 3750 lb capacity is a good choice if staying with a 16" tires and wheels. The G614 RST is made for the "Regional Service Trailer" industry. The Sailun S637 is another 16" all steel ply carcass commercial grade tire.
Both of these tire require a 110 psi rated wheel if you want the full advantage of the higher rated 3750 lb tire capacity.
And of course the 17.5" wheels and tires for 7k axles is another option. However I'm not a fan of over tiring a tire on a trailer to the point of derating its max performance and reliability.
I sure wouldn't use a ST tire on a trailer that size.