Because of the bottoming out issues discussed at this topic
bottoming-out-question-t607496.html ,i was using 245/70 R16 Bridgestone Ecopia line tires, instead of factory recommended 255/65 R16 size tires of my 2000 QX4. I used them about 55000 Km and didn't experienced any issues. In fact it absorbed the bumps and prevented bottoming out issues a little bit with the larger size and the softer compound of ecopia series.
Recently i wanted to renew the tires but learned ecopia series is not imported recently to Turkey and they had only 2013 production tires. Instead of buying 5 years old tires, i bought 265/70/ R16 112H Nokian Line Suv tires and drove about 3000 Km until now. This tires are also very soft, and i didn't experience any clearence - rubbing issues. There is a little bit difference at the speedometer (speedometer shows about 10 % below i believe). As a review of nokian tires i have to mention the handling of the tires are very well, they're quiet, but the build quality and balance of the tires are worse than bridgestone. The balance of the tires are made with much more weight than Bridgestones.
I have to mention also the look of the car is way better with larger tires. I strongly recommend 245/70 R16 or maybe 265/70 R16 tires with soft compound, if you have bottoming out issues.
You can also check this topic :
01-qx4-largest-tire-diameter-t243937.html