That size will present some clearance issues (fixable) but also likely not roll if you are reduced to bump stops.
You'd also need to find a solution for a full-size spare (won't fit underneath)

For your described use, I would suggest at most 265/65 to avoid the above issues.
E load rating can be found in that size, or you can also use XL rating (opening up more options)

I have "smaller" XL 265/60 (still bigger than OEM) and have zero negative side effects during use, and my matching spare fits easily underneath
my occasional off-roading is sure-footed (A/T tire with snowflake)

Depends how much you WANT the larger size.

^ Spot on advice.

To recap, I run 275/65/18 which is actually just a hair past the limit on max size. 32.1" by 10.8". The fronts are not an issue at all, not even remotely so. The rears have slight rubbing but I did not have to relocate the rear coolant lines to the heater - these can be an issue if you have rear HVAC setup as the pipes run being the rear wheel well liner. I did heat my liner with a heat gun to melt and mould it away from the tire in a couple spots, mainly my rear coolant lines. Now with a few thousand miles on them, there is some more apparent rubbing but it is of no concern. If I were to go with an event taller tire, I would have to get strut spacers to reduce tucking of the tires. I am trying to stay away from those spacers since they reduce articulation a bit. I will add that my suspension, less the struts, is very new OEM with a very good alignment. Old suspension will result in more play and difficulty aligning properly. If suspension bushings are worn then you will have a much greater chance of rubbing when pushing the limits on size.
Also mine are e-rated. I highly recommend looking at Toyo Open Country AT3s. When I was looking they came up as the best over and over. Great A/T tire and not noisy or such. I am happy with how my Bridgestones perform... but with the cracking, never again will I buy them or recommend.

It turns out the propeller sound coming from rear of our LR3SE were from the worn rear hubs.So the front bearings and the rear failed while using the slightly larger than orm Hankook AT Dyna All Terrain tires.
When we first put those tires on 37000 miles ago I felt that they put more resistance or strain on the rolling affair. Now back to oem size Bridgestone Alezia Tires and replacedbearings in rear the car is back to being smooth again.The AT tires sure looked good but lasted only 37k and these Bridgestone look good too.