Max without rubbing? Max without rubbing when the suspension is compressed? Max which will fit in the spare tire well if you want a full size spare equal to your tires on the road?
Your stock tire is 205 mm wide and 27.3 inches tall. The optional wheel and tire package has 215/65R17 tires which are 215 wide and 28.0 inches tall. You can do a 215/70R16 tire on your 16 inch wheels which will be 215 wide and 28.0 tall, the same size as the 215/65R17 optional tire, with no problems.
Next size up is the 225/70R16, 225 wide and 28.4 inches tall, with probably no problems in the wheel wells, but you may not be able to get one in the spare tire well, even if you pull the insulation out. Or maybe you can. It seems to depend on the specific make and model of tire.
Going beyond that in width and height seems to get where you are starting to rub in the wheel wells. But you said stock suspension. If you are interested in or wanting to lift your Patriot, then search the threads for the RRO lift kits and Stu's coil spring lifts.
For what it is worth, going to a taller, heavier tire will adversely affect performance and handling on paved roads. It may help handling on rough roads. It will probably help on trails. The taller and heavier it is, the more adverse effect it will have on gas mileage, performance and handling on paved roads.
I had a split sidewall on one of the stock 205/70R16's on a rocky, poorly maintained road I travel regularly. I wanted a more durable tire for that road. I'm going to 215/70R16 Yokohama Geolander AT-S because it is the same size as the upgrade factory Patrioit upgrade wheel and tire package and will just fit in my spare tire well. The 225/70R16 Geolander AT-S would not. The Geolander AT-S's have a good reputation with those on here who use them.
I considered using four 225/70R16 Geolanders on the ground, and a 215/70R16 in the spare tire position, but decided to have all of my next set of tires the same size. I wasn't changing tires to make my Patriot look "non-stock" and didn't want to adversely affect highway performance any more than necessary, since that is what I do 99% of the time.
I am switching to the 215/70R16 Geolanders as my stock tires wear out/fail. I replaced the first one which failed with a split sidewall with the Geolander, which is now in the spare tire well. I still have five of the 205/70R16's. When I no longer have four of them with decent remaining tread, I will switch to all 215/70R16 Geolanders.
It's a judgement call as to what you want to prioritize in your tire choice.
Some people replace their stock tires soon after buying their Patriots, others wait until after they have gotten some use out of them. Used stock tires don't bring a very high price.
Hope this helps.
