Someone may rate the cooper as 10 ply but it is an eight ply tire. The three sidewall plies are part of the carcass that is also under the tread. From Cooper's site:
"Cooper's proven, class-leading 3-ply “Armor-Tek[SUP]3®[/SUP]” construction contributes to the durability of the S/T MAXX by adding strength to the sidewall and tread area."
Then they add two more polys, two steel and one nylon to the tread cap. So the five added to the tread cap, plus the three ply carcass, equals 8 ply.
Many moons ago, it took 10 plies to make a E rated tire; however, with the invention of new high tech compounds, E rated can less than 10 and usually seven or eight. (Maybe even less as new compounds come on the market.)
Telemike: Just remember, one time off road on sharp sidewall biting tires, could make the difference between three ply vs. two ply sidewalls.