Tire size 2000 Chevy 2500 4x4

I have recently purchased a 2015 Adventurer 89RB.My truck is a 2000 chevrolet 2500 crew cab.This truck is the old body style of the 90's. With the existing tires I am on the edge of exceeding the max tire rating . I was wondering if anyone knows of the max tire and or rim tire combo to boost my existing rating. My existing Goodyears are 245/75/16. Mounted on stock aluminum rims. 16x6.5. That being said I see alot of people running 265/75/16 on those same rims. Chevrolet did not allow alot of front wheel well space on this series of body style.Any thoughts. Thanks.