Inversions higher than third
Inversions higher than the third require extended chords; the fourth inversion requires a ninth chord, the fifth an eleventh chord, etc.
If you're working with extended chords, there are more than two possible inversions. For example, the third inversion of a seventh chord puts the seventh in the bass; the fourth inversion of a ninth chord puts the ninth in the bass.
First inversion (A6
Second inversion (C6
Third inversion of F7 chord (E♭4