Can a wild and scenic river have more than one classification?

Yes.  There are three classifications (wild, scenic and recreational) that may be applied to a particular river segment. Distinct segments along the designated reach may contain differing and non-overlapping classifications (wild, scenic, or recreational), e.g., a 100-mile wild and scenic river may be classified as wild for 50 miles, scenic for 30 miles, and recreational for 20 miles.

Source
Interagency Wild & Scenic Rivers Council