First and foremost I don't know what kind of system you're working with which will radically change any suggestions I make. So any comments or edits made by OP will reflect later. However, the following systems have some analogous merit:
The obvious herein lies. In D&D, the editions vary greatly in what multiclassing involves:
- Splitting all XP evenly over all classes
- Picking which class gets the next level
- Choosing at char-gen which (up to) two classes you'll have ever, and divide level-based advantages over the two evenly.
All of the above include sharing the ideological restrictions of all classes to retain their abilities but are ultimately full of Ethical Contortionist moments and quickly get discarded as the only mechanical disadvantage to any class except conflicting alignments to get in no matter how the character acts.
L5R is technically a class based system and would most follow the caveat of D&D.2 for splitting classes but its system includes explicit (dis)advantages that can only be chosen at character creation. Some disadvantages can be stamped onto a player for no reward except RP fun. Some advantages can be bought for a steep inflation in play, but all at GM discretion.
Now what sets L5R apart from most class-based systems is that the skills you train don't need to have anything to do with your "class". You can have a character advance through a warrior class and never put points into any of the skills that school starts you with. I have quite literally played a character with a bushi (warrior) school, and put about 3/4 of my XP into social skills because he was supposed to be a wolf in sheep's clothing. My school advanced because characters have "Insight Ranks" that are based on the sum off all traits and skills, not just the ones it puts to use. If I really wanted to, I could have had two schools: the bushi and the courtier and divided the points over the skills as an equally effective method in many respects.
One of the few things that I liked about NWoD (or "New" World of Darkness) is that you could take as many disadvantages as you liked, but you only received the mechanical drawbacks for them. It was considered that you shouldn't cripple your character for points but for the sake of good RP, if a character needed it the rules were there. Otherwise this isn't a class-based system except for what starting template you pick, and you're not (traditionally) allowed to mix templates without dire results.
One thing I liked about 7th Sea is that other than your character's "Arcana", which if anything fills the blank at all is the only circumstance a character can get points back by getting a Hubris - a tragic flaw (note that it can swing the other way for a singular Virtue) However, in 7th Sea they pull the pendulum the other way and (essentially) make you pay for your disadvantages. They have something called "Backgrounds" which are things you can buy as your character's plot points essentially. Nemesis, Lost Love, Hunted, Mistaken Identity, Fear, and Vow are things that cost you points instead of return them. Granted these increase the amount of XP you receive and could be worth more to you in the long run. However, the XP is only granted when your background causes the party problems as part of the story and requires resolution so it's a brute force method of making players earn the points.
In this game there aren't classes per ce because a character's roles tend to be anchored in things they buy at creation. Mostly this is because they rely heavily on advantages bought when the character with the exception of 'Swordsman' Schools which can be bought later. With this game you are fairly branded by how your char gen goes because buying access to things you don't have is quite expensive. This however doesn't mean that the skills are not expansive. As long as you can afford it you can generally have as many different abilities in parallel as you want.
Warhammer Fantasy has a very modular class system called Career Paths where you can stay in any given class/career as long as you want but there will be a point where you've bought everything and you need to move on - whether along the same path/tree or if you start something new and work from there. Granted, if you don't finish what you've started you can't access it until you revert to that class and you restore it as though you never left. Ultimately this is designed for long term play and char-gen is the tip of the iceberg rather than the base of the pyramid, but you can switch "classes" almost at a whim but there are barriers to entry.