Tires and Wheels ? What Sizes to Use.

[JP2120]

I have a 71 1/2 ton with the factory rally wheels in a size 15 with 5 lug. What is the fattest rear tire you can run with the stock suspension.
I am also looking for some tires once I get this figured out.
It has an open Diff currently but I have a series 3 carrier that will hold 276-343 gears. I have 30 inch tall tires now and don't want to buy gears untill I know what size tire I will be running.

I have also heard of a mod you can do in the back that will allow a wider tire to be used without tubbing or narrowing the rearend.

All tips will be appreciated.
Duke