Is it possible to achieve 9th level spells in 3 different progressions?

With just a little shenanigans, you can get 9th level in 2 progressions. I think Wizard 3 / Druid 3 / Mystic Theurge 10 / Arcane Hierophant 4 does the trick (If I am not mistaken – no books on me right now – one can enter MT way earlier than 6, so no biggie).

But can it be done for 3 progressions[*] on only 20 character levels?

[*] Should have a spell progression with proper spell slots up to 9th level. There is no problem if there are gaps at lower [1 ~4] levels. Things that just add to spell lists (like mother cyst, bonus domains, etc) doesn’t count.

Prestige classes allowed from any 3.5 official publication, including dragon magazine. Assume fractional stat advancement (save, BAB), alignment changes as you see fit,

Forbidden: 3.5 FAQ, negative level shedding, pun-pun, DCFS, Unearthed Arcana.

Tiebreaker are the most extra spell progressions that haven’t reached 9th level beyond the 3 required.