Does this works?

[With a box]

race: Dragonwrought Kobold ,old age
Class: focused specialist conjurer 5/something 1(can I get a feat at level 5?) and take ACF spontaneous divination at level 5.
feat: Versatile Spellcaster, heighten spell and improved heighten spell
skill spellcraft 20,(+9 ranks
+2 synergy from Knowledge(Arcana)
+2 masterwork tool
+7 Int mod)
1.Basis: at n=1, he has three conjuration spell slot.
2.Inductive cab if we assume he has three Nth level conjuration spell slot.
a) marge two of Nth slot to cast (detect magic improve heightened to N+1 level spell)
b) as he can cast N+1 level spell, he automatically get three (N+1) level conjuration spell slot due to being focused specialist conjurer.
c) and even if he stop using Versatile spellcaster, the spell slots self-sustainable.

Since both the basis and the inductive step have been performed, by mathematical induction, he has three Nth level conjuration spell slot for all natural N. Q.E.D.,

if we use less cheese(not use dragonwrought kobold to get epic feat) and use ordinary highten spell, then we can get 1~9th level speciallist spell slot.(3 per each level)

[Rebel7284]

There exists a RAW reading in which this trick works (I think traditionally it has been done with Elf Generalist)

With that said, there is nothing here that is remotely RAI.