I think you will find most are going to G rated ST or E rated LT tires. I have run LT's on my 5W's for years with out issue. I currently have an 11K 5W 2017 with LT's. Ask at a good tire shop what they recommend. This is pretty general as what kind of unit and weights will help answer more.
2015 F350 FX4 SRW 6.7 Crew, longbed - 2017 Durango Gold 353RKT
2006 F350 SRW 6.0 crew longbed sold
2000 F250 SRW 7.3 extended longbed airbags sold
2001 Western Star 4900EX sold
Jayco Eagle 30.5BHLT sold, Layton 24.5LT sold