largest tires for 2008 H2

[ken.j]

Appreciate the suggestions.
By way of an update, I fitted 325/60/20 Nitto Terra Grabbers on my stock rims ( I could n't find better looking or made rims locally) to my H2 and had some rubbing isssues on right hand turn ( not even at full lock), but at speeds over 55MPh, a drone kicked in which you couldn't tune out.
As most of our driving is highway, I went back to the tire shop who have a 30day no quibble guarantee and mentioned the drone. Apparently they have had other drone issues and swapped back my stock rims without fuss - nice guys to deal with.
I liked the look of the grabbers as although only one inch wider that stock (305/60/20 Goodyears) the tread area was wider and gave the truck a more aggressive look.
I still want to fit wider rims ( with correct backspacing to push the tire out and not back) and wider/taller tires ideally without lifting but cannot live with the drone on a daily basis with highway driving.
Maybe I am looking for the impossible but would still apreciate suggestions from any members who have succeeded here.