Chord names don't go any higher than a 13th. If you add another 3rd interval above the 13th degree, it takes you back to the root note of the chord. You can create many more variations on 13th chords and other extended chords by using various combinations of alterations to the 5ths and 9ths of the chords.
Two of most common altered thirteenth chords are the 13#9 and the 13b9.