I am considering purchasing a 2013 Model S P85+ that comes with free supercharging. Does anyone know if this model can accept V2 or V3 supercharging?
When you ask, "accept", do you mean can I plug it in and it will charge? If so, yes, you can.. Car will throttle down to is possible charging speed, even on fastest Supercharger. But its batter will not charge at V3 speed. If its the original battery (it may not be the original battery that came in it), it might charge V2 speed. There;s a slim chance that you can tell what battery is in it. Being the right side front wheel, most 13+ cars have a white tag that show Battery is "A" or "B". We don't know the count, bet it was common for 12-13 batteries to run into problems and were replaced free under warranty. So, the '13 you are looking at might have had the battery replaced with newer, even well have 2014 or 2015. Just don't know. And there's no guarantee or expectation that the tag is there/was there.
My two '13's had the white tag. One of my '13's a P85 had the battery replaced in Oct '16 with an upgraded battery. It was still an 85, even though cars were getting 90's.
On a few occasions, Tesla has been known, (no promise or guarantee that your service center will do it) printed or emailed service records to a new owner. Many have reported here that before they bought a used Tesla they tried to get the records and Tesla declined. Not policy to provide. But after they owned it, a few said, they got them. From those records, you might be able to tell if the battery had been changed and when. Again, no promise or guarantee.
If you can get it to a Supercharger and see what 80 or 90% charge is, you can guessimate what total charge would be. You know, we very seldom charge to 100%. But knowing what you get at 80 or 90% will give you a warm and fuzzy if the car is in good battery condition. These days with gas going up & up, buying a used Tesla is a good idea.
P85+ generally had staggered wheels (wider on rear) and you could not rotate but back to back/front to front. And they were 21". People went through tires quickly with 21". These days, if it was a car I was considering, I would be willing to look for 19" to put on it and spend less going through tires. And they heck with 0-60 in 2.8 seconds. Just my two cents. Likely easy to find a good set of 19" too.