I'm running 31 X 10.50 tires (Wrangler MT/R's).
I'm running 15 X 8 rims, with 2.75" of backspacing.

It all works great.  No problems.

I will be going to either 33 X 12.50's or 35 X 12.50's with the same setup.

i have ford f100 wheels, 15"x8" and 3"back spacing.
with 31"x10.50" wrangler MT/Rs, i had no problems with touching of the chassis or anything else. bumpsteer was minimal. (exactly the same as running 235/75R15 on stock 5.5" wide zook rims)

i now have 33"x12.50" wrangler MT/Rs on those rims, and the tyres will only just touch the chassis at full lock. i think its time to adjust the steering stops.

i think with a 2.75", 2.5" back spaced wheel, you will not have this problem.

only other problems are to do with the amount of flex your rig has and if the tyres clear the body, guards and or firewall.

weaver, if you plan to run 235/75R15 tyres, then go for a 15x7 rim. any tyre less than 10.50" wide (a 31" tyre) doesn't need a wider rim. if you go for a 31" or bigger, then go to a 15x8 rim. some people mount the 235's on standard 5.5 rims, may rub a bit.

if you go for a 15x7" rim, you can mount 235's or less, and you can get away with a 31" on there too. so a 15x7 has a bit of give either way.

backspacing. 3" should be good enough with a narrow tyre, as my 3" BS wheels let the 12.5" wide tyre touch the frame. to be safe, try a 2.75" BS. also with such narrow tyre sizes, bumpsteer should not be more than standard, even with the 2.75" BS. anything less, such as a 2" or a 1" will make the actual wheel stick out more, will result in more bumpsteer, with some times premature wheel bearing wear and failure. same as using wheel spacers.

my front wheel bearings wore out partly due to larger tyres (bigger size and mass) and running a locker on road. thats about all.

hope this helps.