This is something that came up at my last game, hoping someone can set the record straight. I'm a Lvl 9 AT Rogue who has just dipped 2 lvls in Wizard.
According to the Multiclassing spell slot rules, I am now basically a Lvl 5 caster (9/3) = 3 + 2 = 5 which gives me access to Level 3 spell slots.
It was brought up in my game this week, that this does not mean I can learn level 3 spells as neither of my classes has gotten to the correct level. Now I agree with them from a Wizard perspective as in the PHB it says:
Learning Spells of 1st Level and Higher
Each time you gain a wizard level, you can add two wizard spells of your choice to your spellbook for free. Each of these spells must be of a level for which you have spell slots, as shown on the Wizard table.
So on the Wizard table, sure I don't have enough spell slots for level 3 spells.
However, in the Arcane Trickster chapter of the PHB:
The Spells Known column of the Arcane Trickster Spellcasting table shows when you learn more wizard spells of 1st level or higher. Each of these spells must be an enchantment or illusion spell of your choice, and must be of a level for which you have spell slots. For instance, when you reach 7th level in this class, you can learn one new spell of 1st or 2nd level.
Might seem similarly worded, but it's just that part where it says must be of a level for which you have spell slots...
Well I do have level 3 spell slots, so the question is, at this level can I learn level 3 spells?
Potential Duplicate
I do not believe this is a duplicate for one reason. All of the other classes, Bard, Paladin, Ranger, Druid have their own spell types and spell lists. The Rogue AT specifically uses Wizard spells. In this case, if I'm multiclassing into Wizard, I feel like there would be some form of stacking mechanism rather than treating them separately as we're pulling from the same spell list. I also feel that in this case, multiclassing into Wizard would be a spell casting disadvantage in a way, which seems counterintuitive.
Normally, an AT will gain 3rd level wizard spells at level 13, in this case, having dipped 2 levels in Wizard, I have access to 3rd level spell slots at level 11, but now continuing my AT level progression will not unlock level 3 spells for 4 more levels.
At the time I assumed taking a few levels in Wizard would hasten my progression to higher level spells, when it has in fact slowed it. Sure I have more cantrips and level 1s, but no additional level 2s or 3s to show for it.
Each level in AT allows you to swap one spell for another spell that you have spell slots for. I would read that as being able to gain a level 3 wizard spell at my current level.