This may be for nothing, but here is a guideline for the MC parameters I use in my game. Maybe someone playing 5e who want to limit their PC's exposure, offer MCing in a "controlled" fashion, and/or prefer an older/more AD&D flavor to their games might be so kind as to try them out and let us all know how they work in a 5e game.
1. Any PC race (including humans) may multiclass, within the following parameters.
2. No character [PC or NPC] may MC more than two classes at any given time.
3. At least ONE of the classes must be the following ["base"] classes: Cleric [default Life Cleric? I think any domain makes sense here. Given polytheistic religion and all], Fighter [default Champion], Mage [default "Wizard" of my setting, let's say Evoker since that's what they used in the Basic rules, right?] or Thief [default "Rogue" for my game world.]. These are the archetypes with the broadest scope flavor/fluff-wise, so learning/mixing in with them makes the most sense/is easiest to justify. You can go to the Mage's guild or find a kindly mentor wizard and learn to be a mage. The specialist schools are something you learn later. The Thief can learn to use a sword/be a fighter, but becoming a Battlemaster or Eldritch knight takes more time/attention than that. etc...
4. MCing may be chosen at level 1. In which case, the PC is levels 1/1.
-- 4a. If a character does not begin as MC at level 1, they may roleplay toward picking up another class which they may "pick up" at every/any 5th level (5, 10th, 15th, etc...). This allows for the story/rp MC'd characters, a la the "fighter who finds god and eventually, becomes an actual cleric" example from way back in the thread, but a ton of other possibilities exist here. Essentially, any PC who takes the time and effort to try, learn, train to develop the abilities/skills of a completely different type of life/adventuring "profession." Note that at 5th level a player does not just decide to take another class and *Poof* you got a god's attention, you know how spellcasting works, you pick up a set of thieves' tools and go to town. You have to RP this shift in/addition to your interests and invest the time/effort/gold spent on it.
-- 4b. When taking on a second class after 1st level, the character begins the new class as level 1. If this class is a spellcasting class or has any other "magical" powers (e.g. channeling divine), the "caster level" of the character is the level of their magic/casting class, NOT the character combined levels.
5. The following classes are NOT available to MC. They involve in-setting organizations, specialized or consuming training, and/or well-guarded secrets that is simply too specialized, time-consuming and/or intense to permit the amount of time and effort needed to learn/master another class. These are: Barbarian [a class/human race combo, only, in my setting], Bard, Druid, Paladin.
-- Though they exist in the setting, I've never had someone play them, but Monks are in this list as well.
-- In light of the 5e class list, though they've not yet made an appearance in my particular setting, my feeling is Warlocks go here also.
-- Given 5e's lack of General v. Specialist mages, I suppose for this experiment, we will say any variety of "Wizard" is available to MC...though I can not say, at this time, how that would effect flavor in my particular setting, give it a go and see what happens...and in the absence of a generalist wizard, I don't really see another option without going "Illusionists, yes. Necromancers, no. Abjurers, yes, etc etc..." So, we'll just not do that right now for simplicity's sake.
-- 5a OPTION. For characters that want to MC into one of these "initiate" classes the following option may be presented: The Fighter who "becomes" a Paladin, the [Hedgey] Mage initiated as a Druid, the acrobatic rogue who wants to study some martial arts, etc... the former class abilities are lost/eventually forgotten from lack of use and combine with the new class. The character becomes the new class at half their former level [rounded down]. Note: not half of the level they would otherwise become. So the 4th level Fighter who has RP'ed their way to become a Paladin, which would be their 5th level, becomes [half of 4] a 2nd level Paladin.
--5b OPTION: For character that want to MC out of one of these "initiate" classes the following option may be presented: The Paladin that falls/looses their faith and becomes a Cleric of some other deity, the Monk who vacates their training upkeep to study the mysteries of the Mage, the Fey-Pact Warlock who wants to get out of their pact -eschewing magic and capriciousness for the sword and honor- to be a Ranger, etc. etc... in addition to those of your former order/organization/affiliation might well wanting to hunt you down...the former class abilities are lost/forgotten/rejected completely. The character becomes the new class at half their former level [rounded down].
-- and yes, once out of their former "initiate" class, the new PC may then apply #'s 3 & 4a, as available [every 5th level thereafter] as normal, eventually becoming MC'd with [up to 2] different classes, if such is the character's journey through life.
So, MCing Yes [in my world/for this experiment]: [EDIT for clarity] One of the two classes must be: Clerics: any domain. Fighter: Champion. Wizard: Evoker. Rogue: Thief.
Other classes that can be MC'd with: Fighter: Battlemaster, Fighter: Eldritch Knight, Ranger: any, Rogue: Assassin, Rogue: Arcane Trickster, Sorcerer: any (no such class in my games, but they're in 5e, so we'll put them here for now), "Wizard": any school/tradition [In my setting/games, this list also includes an Acrobat & Psychic classes, though we don't have psionics for 5e yet].
MCing No: Barbarian, Bard, Druid, Monk, Paladin, Warlock.
What do folks think of that? Let's see how that goes in 5e play.