I'm running 225/75 on 16in. I have slight rub on the pinch weld but I'm gonna get rid of it. Mathematically 235/70 is smaller than what I have so it may rub it may not. I am using American outlaw buckshot wheels though that have a negative offset which pushes the wheels out giving it a better stance.

https://www.discounttire.com/buy-wheels/american-outlaw-buckshot/p/59913

Here's some pictures, it's getting dark here so they may not be the best.

 

I'm in the search as well for new tires and wheels from what I've read and learned in a couple weeks is that IMO the biggest I would put on my pat without rubbing or modding is a 225/70/r16
If you want a little bit wider 235/65/r16 should work
There are also other factors such as how wide the new wheels are the backspacing and offset etc that play a huge roll
Google some tire size calculators and start punching in numbers

I don't want any rub and I refuse to mod my pat so im playing it safe and getting some 16x7 wheels with 0 offset 4 inch backspacing and some 225/70/r16

Keep us posted on the new combo