Obviously (the forum this is being posted in should make this clear), this isn't intended to be used in any game and any DM who allows it is insane, but if I'm reading the rules correctly this should work. If I'm not, please point out where I am wrong.
The trick involves using the 1st-level-Commoner method of Pun Pun ascension: Summon Pazuzu to get a Candle of Invocation, haul a Sarrukh into your presence and force it to grant you Manipulate Form, and go wild. The character doing this must have at least one level in a casting class, but the remaining levels can be anything else desired as long as Practiced Spellcaster is taken at level 3.
Manipulate Form will now be used to grant the ability Bonus Feat (Ex) from the Human Paragon class repeatedly, which can be used to take any feat for which you currently qualify. Take Heighten Spell, Earth Sense, Earth Spell, and Sanctum Spell. At this point, even with only one level in Archivist, the character can Heighten an orison into a first-level spell, which thanks to Earth Spell is treated as second-level, and gets bumped again to third by Sanctum Spell. This means that he can, for purposes of qualifying for feats, cast a third-level spell.
Now it's time for the real fun!
Manipulate Form in a few more Bonus Feats, in the form of Extra Slot and Extra Spell, to taste. Extra Slot can be used to grant yourself up to a second-level spell slot, and the moment you've given it to yourself, you're capable of casting fourth-level spells, which means that you qualify to use Extra Slot to add third-level slots. Extra Spell ensures that we're continually adding spells of the highest level that we actually have slots for, because we can always cast spells two levels higher than that, and the feat lets us learn any spell up to one level lower than the highest we can cast.
As the character starts gaining spell levels of questionable height, his ability to actually cast the spells within them comes into question. Is his main spellcasting stat high enough to make use of the slots in question? No problem! Human Paragon also has the Ability Boost (Ex) class feature, which we can Manipulate Form in to raise whatever ability we desire by 2 points, as often as is necessary. Thus, it's assured that the character retains the ability to cast any level of spell for which a slot is obtained.
For bonus points, you can do this to any 4 spellcasting classes (granting extra copies of Practiced Spellcaster where necessary) and follow up by taking 16 levels of a random full-BAB class, giving a quad-9 Gish (4x iterative attacks at 20). If using UA's partial BAB and Save gains, then you have a minimum of +2 BAB at level 4, +3 at 6, etc, so you can fit in more spellcasting classes before you have to switch over to a full-BAB class for the rest of your career.
As a side-note, this could be considered an alternate way to bost part of Pun Pun himself, as I've not seen Human Paragon's Ability Boost used in the theoretical builds for him, though it seems to be the least round-about method for improving his abilities without having a handy snake at his side. Since Pun Pun is capable of granting himself a free level at any time he likes, he can gain one level of any spellcasting class, use this method to grant himself as many spell-slots as he likes in said class along with a CL equal to his current HD, and make sure that he knows all of the spells legitimately, rather than granting them to himself as SLAs. (As if Pun Pun needs NI spell slots to go with everything else.)