Max Tire size with no rub?

[2017Powerwagon]

I have a 2017 Power Wagon Laramie, I currently have 285/70/17 tires but am looking to see what the largest size tire people have had installed without rub or customization. My experience is that the tires seem to be too narrow and the truck likes to sink on soft ground (dirt mostly) pretty easily. I don't spend much time on sand but don't want to get the wrong tires and have to customize a bunch of stuff. Thoughts?

 

[H3LZSN1P3R]

You have a 4th gen not a 4.5gen but this question is covered 1000s of times 35x12.5 will fit with little to no rubbing depending on tire brand