[RPG] Is it unbalanced to allow multi-classing with a lower ability score


The PHB states that the pre-requisites for multi-classing are as follows:

\textbf{Class} & \textbf{Ability Score} & \textbf{Minimum} \\ \hline
\text{Barbarian} & \text{Strength} & 13 \\
\text{Bard} & \text{Charisma} & 13 \\
\text{Cleric} & \text{Wisdom} & 13 \\
\text{Druid} & \text{Wisdom} & 13 \\
\text{Fighter} & \text{Strength $or$ Dexterity} & 13 \\
\text{Monk} & \text{Dexterity $and$ Wisdom} & 13 \\
\text{Paladin} & \text{Strength $and$ Charisma} & 13 \\
\text{Ranger} & \text{Dexterity $and$ Wisdom} & 13 \\
\text{Rogue} & \text{Dexterity} & 13 \\
\text{Sorcerer} & \text{Charisma} & 13 \\
\text{Warlock} & \text{Charisma} & 13 \\
\text{Wizard} & \text{Intelligence} & 13 \\

Would it be unbalanced to allow multi-classing with a lower ability score?
The +1 modifier comes at level 12, not 13, so multi-classing at 12 makes more sense to me.

For context:
Currently I am playing a Wild Magic Sorcerer (level 3). He has just discovered his magic and set out to share his wonderful gift by cleaning up Faerûn (he is a germophobe named Pyorelle and makes heavy use of Prestidigitation). He is extremely curious about his magic so he has been reading every book he can find about magic. I never intended to multi-class, but the character has developed to go down a more studied route.

RP-wise, it makes perfect sense for him to take a level of Wizard soon, but mechanics-wise his INT is currently 10. RAW he would need to wait until hitting level 9 to multiclass (increase INT at level 4 and 8, then multiclass at 9), which seems way too long for the amount he has been studying and researching magic for the past level.

As a note:
I am working with my DM on options. I am not asking for opinions on whether the DM should/shouldn't allow an early multiclass. I am more wondering what balance would be broken by allowing multi-class with a lower ability score (but not game-breakingly-low).

Best Answer

On your particular case, I don't think it is game-breaking to allow multi-classing at INT 12.

Since you are considering multiclassing for roleplay purposes, it makes sense to allow your character to get one Wizard level if you have INT 12. I don't see any particular issues with allowing a single level multiclass using the conditions you proposed. Your DM may rule that you cannot get further levels with only INT 12, since your Intelligence will stand below the average of a Wizard.

You might want to consider the Magic Initiate and Ritual Caster feats from the Player's Handbook (pages 168 & 169) as options to fulfill your roleplay as a "student of magic". Remember that you need at least INT or WIS 13 for the Ritual Caster feat.