RAW can a Eldritch Knight 9/Wizard 2 multiclass cast 3rd level spells?

Title is the main question, loosely an extension of a previous question I’d asked about Eldritch Knight/Wizard multiclass and their access to spells.

From previous question

From that post and other research online my understanding is that spell slots and the ability to cast the spell are different things.

Spell slots are fairly straight forward as laid out in the multiclass section of the PHB and, additionally on p.164, this line seems to be the key for casting ability (emphasis mine):

You determine what spells you know and can prepare for each class individually, as if you were a single classed member of that class.

Eldritch Knight has spells known and by the given example of level 9 can learn and cast up to 2nd level spells based on their table. Wizards have their spell book from which they prepare spells for the day and at 2nd level their table allows them to prepare 1st level spells. From this and taking the “prepare for each class individually” literally it seems that the spells known from EK would be at most 2nd level and from the Wizard levels at most 1st, so the answer to “can I cast 3rd level spells?” seems to be No.

The possible exception

Now, the only point I’d really think needs clarification is the fact that the Eldritch Knight uses the Wizards list of spells to pick from for their spells known. I think RAW the comparison is ultimately Fighter vs Wizard and thus clearly not the same class but a case could certainly be made that an Eldritch Knight would understand the basics of magic by 9th level and it seems weird that they wouldn’t gain spell levels any faster by taking levels in Wizard. In fact, if this player in particular at EK L9 wanted to take levels in Wizard to expand their spellcasting, which it certainly would do as then they could prepare from their book as well, they wouldn’t get 3rd level spells until EK9/Wizard5. Eldritch Knight gains 3rd level spells at 13th level so, if that was the only goal, it’s actually faster to just keep leveling as an Eldritch Knight, needing only 4 more levels, rather than taking 5 levels of Wizard.

Similar but somewhat unanswered questions also from Stackexchange are:

  • this one about Arcane Trickster 9/Wizard 2 which is probably the most direct comparison as the Arcane Trickster has nearly identical wording to the Eldritch Knight in that they pull from the Wizard spell list (though EK is based on Evocation or Abjuration while AT is based on Illusion and Enchantment).

  • this question seems to be asking the same question I am indirectly with their main question being (emphasis mine):

Now, since in that peculiar case the spells are from the same spellcasting class (the wizard), can I learn spells of higher level, for which I have spell slots, even if my single class level could not permit it?

Both of the above questions don’t have a selected answer by the asker but both are marked as duplicates to a question clarifying multiclass rules for spellcasting. The answer to that question seems to be based on the earlier quote from preparing spells as a multiclass (here again for emphasis):

You determine what spells you know and can prepare for each class individually, as if you were a single classed member of that class.

The book gives the example of a Ranger 4/Wizard 3 which clearly are different. The real question then is if an Eldritch Knight, or an Arcane Trickster by extension through the same logic, multiclassing into Wizard are exceptions to the above rule since they already use the Wizard spell list. Again, my understanding is that the answer is No.

Should I allow it anyway?

While I believe the above is true… it’s frankly kind of lame. The player in question agrees for obvious reasons and I’m trying to think what I can do about it without making insane balance considerations. If we go off the assumption that the above is correct then the L9 Eldritch Knight would need 5 levels of Wizard (or 4 more if they just kept leveling as an EK). If I allowed ignoring the “as individual classes” bit and instead went with “you have the spell slot you can prepare/learn it” then I’m effectively allowing 3rd level spell casting at half the needed levels and everyone knows 3rd level is where the big jump in power comes for spells. This seems like a big balancing issue and causes all kinds of other problems if other characters try to use the same logic and if I only allow it for EK/Wizard or AT/Wizard multiclasses that’s edging toward special privileges for the player. My only real counterpoint to that is how weirdly well Warlocks and Sorcerer’s tend to mesh together and, while RAW, feels like a similar exception if a player wanted to play the infamous Sorlock.

My Conclusion

From all of the above the answer seems to be No (though personally that’s just kinda lame) and would just like input to make sure I’m reading the rules correctly.