Re: John Deere 316 garden tractor 3pt.
At first, I thought the rear frames were not similar, as I purchased a frame mount trac-vac, that came off of a 425, and to cut and weld, to fit my 318, which the frame is the same as the 316. Not so sure now.
The 3 point hitch kits are different part numbers, on the JD site, but some of the individual part numbers are the same. A very popular ebay hitch manufacturers seller, sells one they say
fits both the 316/318 and the 400 series.
So I would say "most likely".

These guys will tell you for sure.
http://www.weekendfreedommachines.com/
Can you get the hitch at a good price? I would swear those hitches are made out of gold. I can't justify 1/3 the cost of the tractor, for a 3 point hitch.