I took this question to the manufacturer and here is Michelin's response:

I drive a 2010 Toyota 4Runner which originally came with P265/70R17 tires and Toyota recommends 32psi for these tires. I now have LT265/70/R17 (E Rated) Michelin LTX M/S2's. Should they be inflated to a different pressure? The GVWR is 6300lbs. Also? Should I increase the pressure when towing a 4000lb trailer? Any help would be appreciated.

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When installing a different size than the original equipment tire, all vehicle manufacturer specifications must be maintained. The replacement tire should be inflated to provide the same load capability of the original tire size at the manufacturer’s recommended pressure. By changing to the LT rated tire your pressures should now be at 50PSI. You do not need to change the pressures for extra loads or towing.