It's not possible to do it "naturally".
We do need double sharps pretty often, and double flats at times. But double sharps are most commonly needed to keep a melodic or harmonic minor scale diatonic (I'm using diatonic in the literal sense of "through the tones", or having one of each letter).
Let's say you've got a key signature of B, five sharps. And you're in the relative minor, G#. The harmonic minor raises the seventh degree, which is F#, so we need Fx.
If you're writing a melody, you'd have no need for a triple-sharped F, because you would just write G#. So the only reason you'd need to raise that Fx again is to accommodate a particular chord.
Since chords are built in thirds, you cab consider each chord tone:
- it can't be the root, because they're never raised
- it can't be the third, because a raised third is a sus chord, which uses the fourth
- it could be the fifth, for an augmented chord
- it can't be the seventh, because raising that is the root
- it could be the ninth; #9s are common
- it could be the eleventh, as in a maj7#11 chord
- it can't be the thirteenth, because you'd write it as b7
So the only times you'd "naturally" need a triple sharp is if it's the 5th, 9th, or 11th.
Now we can work backwards:
- if Fx is the fifth, it's a B root. But in key, it's already augmented: B-D#-Fx. We have double augmented intervals, but double-augmented chords don't exist (because it would be a G#m inversion, G#-B-D#)
- If Fx is the 9th, then E is the root. But that means Fx is already a #9.
- If Fx is the 11th, then C# is the root. But that means your Fx is already a #11.