In my experience, there are three kinds of multiclassing.
1) Level dipping. You want some goodies that another class has. Generally speaking, this is the min-max part. I find that most people don't dip into another class for story reasons, they do it for abilities. I want to put agonizing eldrtich blast on my sorcerer. I want my wizard in heavy armor and proficient in Constitution saves. While, theoretically, this can be story driven, I have never seen anyone dip for it done as anything but.
2) Gestalt / Hybrid classing. This tends to be where you have a concept that eclipses two classes. A sorcerer-barbarian, because you want dragon magic and all the rage and physicality of a dragon. A cleric of a diety of magic, who studies arcane magic alongside the divine power. Or a crimson knight - the paladin/warlock hybrid from 4e? There was a huge cultural thing for tieflings with that combination.
So far, the closest we have are some key subclasses. The current, 3e era multiclassing is terrible for a gestalt style multiclass, given how milestones and tiers work.
3) Career changes. You're an old assassin who repents and becomes an avenger, following the holy path. A warlock who forsakes their dark power to help protect. There's no good rules to really represent this - at best, there's the Oathbreaker's method. Again, the current multiclass rules are bad for this, for same reason as the gestalt rules.
I just flat out dislike the current multiclass rules. They're designed to only be worth very rare dips outside your main class which, in my experience, is a technique used to min-max, and I have never seen it used for story reasons. Subclasses handle the gestalt style multiclassing now, and the career changes, while enjoyable, are pretty crappy rules wise. I'd rather handle that personally and come up with something custom for a character when it happens than use the existing rules.
1) Level dipping. You want some goodies that another class has. Generally speaking, this is the min-max part. I find that most people don't dip into another class for story reasons, they do it for abilities. I want to put agonizing eldrtich blast on my sorcerer. I want my wizard in heavy armor and proficient in Constitution saves. While, theoretically, this can be story driven, I have never seen anyone dip for it done as anything but.
2) Gestalt / Hybrid classing. This tends to be where you have a concept that eclipses two classes. A sorcerer-barbarian, because you want dragon magic and all the rage and physicality of a dragon. A cleric of a diety of magic, who studies arcane magic alongside the divine power. Or a crimson knight - the paladin/warlock hybrid from 4e? There was a huge cultural thing for tieflings with that combination.
So far, the closest we have are some key subclasses. The current, 3e era multiclassing is terrible for a gestalt style multiclass, given how milestones and tiers work.
3) Career changes. You're an old assassin who repents and becomes an avenger, following the holy path. A warlock who forsakes their dark power to help protect. There's no good rules to really represent this - at best, there's the Oathbreaker's method. Again, the current multiclass rules are bad for this, for same reason as the gestalt rules.
I just flat out dislike the current multiclass rules. They're designed to only be worth very rare dips outside your main class which, in my experience, is a technique used to min-max, and I have never seen it used for story reasons. Subclasses handle the gestalt style multiclassing now, and the career changes, while enjoyable, are pretty crappy rules wise. I'd rather handle that personally and come up with something custom for a character when it happens than use the existing rules.