Are NPCs who want to gain class levels considered multi-classed?

Question

Consider an Apprentice Wizard from Volo's Guide to Monsters: its spellcasting is the same as a 1st-level wizard, its skills are from the wizard list, and it's proficient in a weapon from the wizard list. Its stat block doesn't have arcane recovery, but that could just be because it's not relevant to combat. Other than obviously having 2d8 instead of the full value from 1d6 for its hit points, and the lack of saving throw proficiencies, it's basically like a 1st-level wizard.

So if you had one join your party, and had it gain a level, would it gain a spell slot and an arcane tradition as a 2nd-level wizard, or would it gain two more skills and two saving throws as a 1st-level wizard?

By the same token, if you wanted to give it some martial ability by giving it a level in fighter, would it be looking at getting proficiency in all weapons/armor, two skills, and two saving throws, or would it only be looking at weapons and light/medium armor and shields (but in actuality not be able to gain fighter levels because it doesn't meet the strength/dexterity requirement)?

What if you wanted to do both of the above, giving it a level in wizard and one in fighter? (or possibly the other way around: fighter first then wizard after, if ability score requirements only let you do that order)

Answer 1

The Sidekick rules can help you

There is something that can help you with an NPC/Monster giving levels; the Sidekick rules. Released in this UA article (also officially in the Essentials Kit) are rules for applying class levels for what is essentially a simplified version of a PC class (either "Warrior", "Spellcaster" or "Expert") to an NPC/Monster of CR 1 or less (which, happily, the Apprentice Wizard is).

It still wouldn't be considered multiclassed

However, if you used the Sidekick rules to give your Apprentice Wizard class levels, it wouldn't be considered a multiclassed NPC because the Spellcasting feature it has would be considered a "monster statblock feature" rather than a "class feature" (because, as a monster, it doesn't have a "class" in the same way that a PC does).

From the Monster Manual (p. 10) under "Special Traits":

Spellcasting

A monster with the Spellcasting class feature has a spellcaster level and spell slots, which it uses to cast its spells of 1st level and higher. [...] The monster is considered a member of that class when attuning to or using a magic item that requires membership in the class or access to its spell list.

This calls out that the "monster" (in this case, NPC) is considered a member of that class (wizard, in this case, as pointed out by the Apprentice Wizard's Spellcasting feature) only in the context of attuning to or using magic items. Because it specifically calls out this context, we can infer that it is not considered a member of that class (because classes are for PCs, not NPCs/monsters) generally. Hence an Apprentice Wizard with "Sidekick levels" would not be considered to be multiclassed.

Answer 2

No, advanced monsters/NPCs with class levels in a single class are not multiclassed

As the DMG describes, you can add class levels to an existing creature to make it more powerful:

You can use the rules in chapter 3 of the Player’s Handbook to give class levels to a monster. For example, you can turn an ordinary werewolf into a werewolf with four levels of the barbarian class (such a monster would be expressed as “Werewolf, 4th-level barbarian”).

Start with the monster’s stat block. The monster gains all the class features for every class level you add, with the following exceptions [...]

The exceptions being that a monster doesn't automatically get starting equipment, it keeps the same hit die size it already has as a monster, and it uses its CR, rather than total levels, to calculate proficiency bonus.

Note that this refers to the rules in Chapter 3 of the PHB, which is the section on classes. The multiclassing rules are optional rules and actually feature in Chapter 6 - and these rules are not referenced by the DMG's guidance. The game does not appear to expect that the multiclassing rules are getting involved here - your monster should get all the class features that such a character gets, which includes whatever proficiencies a normal first level character of that class should have.

In the specific case of your advancing an Apprentice Wizard by adding wizard class levels to it, despite the fact that it looks very similar to a PC wizard already, it is not a PC wizard - it is a "monster" with wizard-like spellcasting. Adding a level of wizard to it grants it the benefits of being a first level wizard on top of what it already had - there's no affordance for it stacking up to produce a second level wizard. The DMG doesn't offer any guidance on how to combine the two Spellcasting features the monster now has, but it would seem reasonable to try and use the multiclassing rules about spellcasting to determine its new capacity in that case. If you add a fighter level, it gets all the benefits of being a 1st level fighter, including full proficiencies with armour and saving throws and whatnot.

At the point you find yourself wanting to add levels to the Apprentice Wizard, it probably makes more sense to disregard the original "monster" stat block and just rebuild the creature as if it were a PC using the normal PC rules. Stat blocks that seem almost directly representative of a PC class, like the Apprentice Wizard (Wiz 1) or the Archmage (Wiz 18), are basically there to save a DM the effort of building those characters by hand. If you start wanting to seriously modify them, rebuilding them fully using the normal PC rules will be more internally consistent and avoids any mechanical weirdness like that discussed above.