What is the fattest rear tire I can put on my 2017 Sportster 883N Iron, on the stock rim, with no mods

 

look at the space between the belt and tire. that will be as much as you can go.

 

Your other limitation is the width of your wheel rim, which I suspect is 3". Check alternative brands of tyre for their recommended rim widths, but also be aware that installed tyre width can be quite a bit different from stated width. As an example I have a 160mm tyre on my Glide, but it measures 167mm wide, over 1/4" wider than spec.

 

Your fender is another limiting factor, there is very little room to spare already with the 150 stock width.

 

Here's a thread dealing with the 170 rear on stock bike.

https://www.hdforums.com/forum/sport...he-sporty.html