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The 5e rules for multiclassing (PHB p. 164) state that your spells known and prepared are based on your class level for each class, but your spell slots are based on your combined levels, which may result in you having spell slots of higher level than any of the spells you know. They provide an example for Ranger 4 / Wizard 3. With respect to Wizard spells known it says:
As a 3rd level wizard, you know three wizard cantrips, and your spellbook contains ten wizard spells, two of which (the two you gained when you reached 3rd level as a wizard) can be 2nd level spells. If your Intelligence is 16, you can prepare six wizard spells from your spellbook.
This combination counts as a 5th level caster for determining spell slots:
you have four 1st level slots, three 2nd level slots, and two 3rd level slots. However, you don't know any 3rd level spells....You can use the spell slots of those [higher levels than you have spells] slots to cast the spells you do know -- and potentially enhance their effects.
Suppose this Ranger 4 / Wizard 3 character with Int 16 comes across a 3rd level wizard spell scroll, and has on hand sufficient material components and fine inks to copy the scroll into her spellbook. Is she allowed to copy the spell? Is she allowed to prepare and cast it?
The rules for copying a spell into your spellbook (PHB P. 114 sidebar) require you to have spell slots of that level.
When you find a wizard spell of 1st level or higher, you can add it to your spellbook if it is of a level for which you have spell slots and if you can spare the time to decipher and copy it.
RAW then it appears that the character, who does have two 3rd level slots, would be permitted to copy it into her spellbook.
And RAW (from the first quote) she can prepare six wizard spells from her spellbook which now happens to contain a 3rd level spell. There is no qualification on the level of the spells from her spellbook that she can prepare.
It seems to me that RAI is probably that she can only copy/prepare spells of a level that she would normally have access to as a level 3 Wizard.
Does my RAW reasoning have any flaw? And would you allow it in your game?