Most of the austenitic, 300-series stainless steels will undergo the transformation to some extent depending on the exact chemical composition, strain rate during forming/deformation, etc.
316 has a higher nickel content than 304, so it does not transform to martensite during deformation as much as 304 does. Stainles steel Type 301, Type 201, and Type 302 transform the most, and therefore, strain harden to higher strength levels than the other austenitic alloys.