Yes. The variables are endless, but yes.
My buggy is a terrible example, but I run 6-1/2# front and 6# rear. The buggy weighs 3850 pounds. My rear tire/wheel weighs 145# each. My fronts have water added to achieve my preferred 58.5% front bias. Front tire/wheel/water is 350# each. That is valve stem about 10:00....valve stem at 12:00 (top) puts that tire/wheel/water at 425# each. (Yes, I have scales....and too much nerd time on my hands). 42's on 20x8-1/2's and that gives me enough footprint for "vertical" climbs and keeps the sidewall stiff enough for steep drops that require steering out the bottom. A 42/17 would be terrible for control, since I'd need higher pressure to limit that sidewall shift which then translates to a smaller footprint and less traction.
More sidewall:
- increased chance of sidewall tears due to obstacle pinches
- less directional control as pressures decrease
- maximum flotation for sand/snow traction
- potentially wider footprint at lower pressure (further increasing sidewall exposure)
Less sidewall:
- increased chance of sidewall pinch flats between the rim and rocks as pressure decreases
- increased directional control due to less sidewall shift
- longer footprint at low pressure with less width increase to help protect sidewall
Now throw in rim width, and you can further screw with all of that

Personally, I think rims should be 2/3 of tire section width\ (or slightly less). On my buggy, the tires are 14.5 section width, so I should be running a 9.66 wheel...but because of the lower pressures and sidewall shift (and the bottomless cracks we have at Sand Mountain), we frequently get rim locked with a 9-1/2" to 10" wheel, so I run a narrower Battleborn Forged 20x8.5" beadlock wheel to prevent that.
With my FZJ80, the 12.5 section width should be on 8.33" wheels, and I think my Racelines are 8-1/2".
Tire pressure is dependent on a dozen variables too....terrain, load, speed, and the tire itself. No two sidewalls are the same, so the pressure that works best for a Cooper may not for a Toyo or a BFG or an all terrain versus mud terrain. And there is ZERO reason to run identical front/rear pressures, those should be based on load.
CAT scales are everywhere, and knowing your overall/front/rear weight is useful. I know my Sprinter is 7420 total, with 3540 front and 3880 rear. I need to weigh the 80 one of these days.