The five numbers have sum $28 + n$ and mean $\dfrac{28 + n}{5}.$ The median is the middle value when sorted, which is $6,$ $n,$ or $9$ depending on the size of $n.$

If the median is $6$: $\dfrac{28 + n}{5} = 6$ gives $n = 2,$ which is indeed less than $6.$ If the median is $n$: $\dfrac{28 + n}{5} = n$ gives $n = 7,$ which is between $6$ and $9.$ If the median is $9$: $\dfrac{28 + n}{5} = 9$ gives $n = 17,$ which is indeed greater than $9.$

Each case yields a valid value, so $n$ can be $2,$ $7,$ or $17$ — three possible values.

Thus, the correct answer is C .