Can you use auto-increment in MySql with out it being the primary Key

Question

I am using GUIDs as my primary key for all my other tables, but I have a requirement that needs to have an incrementing number. I tried to create a field in the table with

Answer 1

I would lean the other way.

Why? Because creating a composite key gives the impression to the next guy who comes along that it's OK to have the same GUID in the table twice but with different sequence numbers.