What is the largest tire that will fit on the rear of an 07 FLHX with the stock wheel without modifications or problems on the road?

 

I believe stock is D402/MU8516 which is a 140mm tire; approximately 5.5" wide. With no or minor modifications you could probably squeeze a 150mm (5.9" wide). You have to check for clearance on the right (brake) side between tire and fender and check clearance on the left (pulley) side for clearance between belt and/or belt guard and tire. You might have to remove or notch the belt guard.

 

150/80/16 on a stock wheel.