Shooting star of mystic fire: infinite CL?

[Irk]

Mystic fire knight (MLK) and Shooting Star (SS) both have the ability improved spell casting, which allows paladin or ranger CL to become equivalent to 1/2 of paladin or ranger level plus 2 plus the CL of another arcane casting class. If we toss a level of wizard into this, we can acquire the feat alternative spell source, which lets us prepare divine spells as arcane. If we prepare our ranger and paladin spells as arcane, they gain "arcane spell casting ability", which means they affect each other's improved spell casting ability. Lets see how this interacts:
MFK 4/SS 4/Wiz 1

Now, MFK prepares a 1st level paladin spell as an arcane spell at CL 3 (wiz + MFK/2)
The SS prepares a 1st level ranger spell as an arcane spell at CL 6 (wiz + SS/2 + MFK CL)
But wait! due to the way in which SS and MFKs CLs interact with one another (since they both have arcane spell casting ability, and thus stack), MFK's CL goes up by 6, becoming 9. Then, SS's Cl goes up by 9, becoming 12. MFK's Cl increases by 12, SS's CL increases by 21, all the way up to infinite CL ranger and paladin casting. Kind of useless, but maybe good with SotAO.

My question is this: does it work?

[Aegis013]

This only works if you assume/interpret that being able to prepare your Paladin/Ranger spells as arcane makes the classes into arcane casting classes, instead of divine, or possibly makes them into both. Which if so assumed/interpreted, should mean you can advance their spellcasting with any PrC that advances arcane spellcasting.

However, I don't believe that Alternative Spell Source, Southern Magician, and the like change the nature of the class. Just because your Paladin has Sword of the Arcane Order doesn't make the class an arcane class. It's still a divine spellcasting class. So I would say this doesn't work, but that's just my interpretation/opinion.

[Irk]

This only works if you assume/interpret that being able to prepare your Paladin/Ranger spells as arcane makes the classes into arcane casting classes, instead of divine, or possibly makes them into both. Which if so assumed/interpreted, should mean you can advance their spellcasting with any PrC that advances arcane spellcasting.

However, I don't believe that Alternative Spell Source, Southern Magician, and the like change the nature of the class. Just because your Paladin has Sword of the Arcane Order doesn't make the class an arcane class. It's still a divine spellcasting class. So I would say this doesn't work, but that's just my interpretation/opinion.

I guess I did not phrase it well enough, but the improved spell casting abilities simply necessitate "arcane spell casting ability", which may or may not be RAW defined. They're definitely not arcane casters because of alternative spell source, but does it give them "arcane spell casting ability"? If so, it does work.

Apart from that, I would agree with you entirely, sorry for phrasing it poorly.