I have been drifting in a decidedly anti-multi-class direction lately, but I have been considering hypoethetical circumstances under which I might find it acceptable or possibly even desirable. What immediately springs to mind is the Renaissance man or woman. I am not, of course, referring to anyone who might exist during the Renaissance, but to those individuals whose talents and skills extended to a wide variety of subjects. They were not mere jacks-of-all-trades, but dedicated experts in multiple fields. For these individuals a multi-class option would make sense. This falls in line with another experiment I was considering when I was planning to write my own Original Fantasy Role-Playing Game-compatible RPG. I wanted to create a neo-retro-whatever-clone that justified all the crazy traditional rules in the context of the game world, just as Empire of the Petal Throne did, but without having to place it in an alien setting. Things such as "level," "alignment," "(character) class," and possibly even "saves" would be utterable in-character at the game table because they would be part of the setting. The only way I could justify it without resorting to a campaign world requiring Tékumel-levels of detail was to frame it in terms of a secret society. Certain rare individuals Renaissance men and women are privy to the knowledge that there is more to reality than what is ordinarily perceived by most. They are inducted by secret ceremony into an organization that seeks to deal with this other reality in accordance with their goals, or alignment. As they increase their experience with the unknown, their achievement in each class of endeavor is formally recognized by an increase in their level within the organization. As they rise, their ability to save themselves from worse threats also rises.
Such ultra-competent individuals would be above the constraints of the traditional D&D class system, but the traditional multi-class system also falls short. Instead, I envisioned a system based on the OD&D elf. Just as an elf decides at the beginning of each adventure whether to function as a fighter or magic-user, gaining experience only for that class during that time, a player character in my game would decide at the beginning of each adventure whether to function as a cleric, fighter, magic-user, or thief (although I renamed the classes to better fit the setting). Player characters could remain in one class as long as they like and switch classes as often as they like (as long as the switch occurs at the beginning of an adventure). Abilities gained from a class are retained, and the best available saving throw or attack roll is always used.
Non-player characters who are not part of the conspiracy do not qualify to multi-class, nor do they gain levels. They gain ranks. Functionally, they are the same, but to mention "levels" outside of the organization is to reveal a secret and raise the suspicions of the ignorant, which is almost everyone. Mentioning "alignment" also raises eyebrows amongst non-members, and discussing spells, monsters, demons, or planes of existence will surely get one branded as a witch and burnt at the stake.
In this conceptualization, all player characters are human and the setting is more Renaissance than Middle Ages (to reflect the rebirth of the sciences and to emphasize human achievement), but exceptions could be made for the rare visitor from the realm of faerie or those hidden worlds beneath the earth's surface.
Hm... Maybe I should revisit this idea and publish it.