Hey,
It *IS* possible, thanks to XDA Dev mickybart.
Not easy process at all though, check [https://forum.xda-developers.com/showpost.php?p=65233973&postcount=3797|this guide] on XDA. Make sure to flash Android 7.1 in the end ([https://forum.xda-developers.com/xperia-s/s-development/rom-naosprom-xperia-s-t3462373])!
Your warranty will be void by doing this. If you run into problems, do not hesitate to ask at that forum (the 7.1 ROM thread.)
PS: Rooted phone is necessary :)
Good luck!