There are some good tire size comparison sites on line where you can input different size tires to see how much difference there is between them. Here is one example I used from Tire Size Comparison
The width of the new tire seems to be the biggest change, everything else looks like it would work well as a different size to use. I don't have any idea how much wider you could go with no problems such as rubbing, etc.
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Just want to chime in regarding my Michelin Defender LTX tires. I put them on at 24k miles over 2 years ago. Currently I'm at 64k miles and I still have in between 7/32 -8/32 tread life on them. I drive like an animal and I love the torque vectoring around corners. Best tires I've ever owned for this type of vehicle! Can't recommend them enough. I've never hydroplaned nor slipped much in snow. They give me all the confidence in the world. If you have the money, do yourself a favor and buy them.
If you're looking for a set of new wheels (rims and tires) I have some input as to the maximum width and offset. I have 10" wide rims with 35mm offset and 285/45 tires. It's does scrub against the inner plastic wheel arch when in reverse and full lock on the steering. So with 10" rims, don't go lower than ET40 (offset) and stick to maximum 275/45 tires and all shall be fine.
I went with a set of 255/55R20 Goodyear Assurance ComforTred Touring tires on mine & have had zero clearance issues. You just need to be aware that your speedometer is going to read slower than actual speed when going with a tire that is any larger in circumference. These make my speedometer read around 4% slower than actual speed. I personally wouldn't want any wider or taller tires than these mounted on stock rims for this vehicle... I did a writeup on the tires if you're interested. Honda Pilot - Honda Pilot Forums