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I'm aware of an FAQ-based argument against Persistent Time Stop that also rules out Extended Time Stop. However, is there any RAW argument against Repeated Empowered Maximized Time Stop? By my (hopefully correct) calculations, a Deity casting this via Alter Reality would get 14 rounds of Time Stop for 10 rounds of rest, letting them persist the spell without actually persisting it (because they can cast it again during the spare 4 rounds).

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You can...

There is nothing preventing you from applying Repeat Spell, Empower Spell, or Maximize Spell feats to Time Stop.

... but you would not get the desired effect

First and easiest, Maximize Spell doesn't maximize additional portion of the spell gained through Empower Spell. Your lower cap would be six rounds - five from maximized portion of a spell, and one from empowered one, if you rolled poorly - and you should always assume you rolled poorly if you want a guarantee.

Second, Repeat Spell says

A repeated spell is automatically cast again at the beginning of your turn in the following round

so there are turns of all opponents between those two castings. And you want more than ten rounds of uninterrupted apparent time.

Third, and that's just my opinion on a subject, not a rule set in some book. You probably shouldn't be able to cast Time Stop from Time Stop. Or, at best, you may apply the better result of the two.
This is because, those rounds are basically the effect of the spell and not its duration. It's how fast you are, not how long it lasts. Forget about Repeat Spell for a moment. You just have two or three Empowered Maximized Time Stop spells. Say your first Time Stop went out with six in its 'duration'. You are now that fast. After three rounds you cast another. It comes out with seven as a 'duration'. You are now a bit faster for the remaining 'duration'. Is it OK to give you that bonus round for being faster? OK, you have it. Is it OK to say your resulting quickness is now that fast to give you ten rounds total of apparent time? I don't think so.

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