Would you be okay with class abilities that explicitly addressed multi-classing?
What exactly are you trying to address about it? That players shouldn't do it? That it doesn't work too well? Or that it works too good? Or that there aren't enough hoops to jump through? I think you need to be more specific about what it is you are trying to fix before you start fixing anything. That goes for any edition, any system, any problem.
Cinematic Defence: a single-classed Fighter may use her Proficiency Bonus instead of her Dex bonus when calculating AC; a multi-class Fighter may only use a +2 bonus instead of her Dex bonus.
First, terrible name. How about Armor Expertise?
So why would a Fighter with a higher Dex bonus take this? They wouldn't. At least not until their Proficiency Bonus exceeded their Dex bonus, or at least the limitation of the armor they wear.
Which leads to another question: When/how do they take this? Is it automatic for all Fighters? If so, at which level? Or is it a Feat? You need to explain this more clearly, or give it some more thought.
Divine Agility: a single-classed Paladin may use her Charisma bonus instead of her Dex bonus when calculating AC; a multi-classed Paladin may not.
So why would a Paladin NOT take this? Because most Paladins are going to have a higher Charisma bonus since many of their other abilities rely on this attribute already. And if they multi-class, then they suddenly lose this ability, not just make it worse like the one for Fighters above? That's inconsistent.
Personally, I like the idea of hybrids, not just in D&D 4e, but also in Pathfinder, and to some extent AD&D (1e & 2e).
D&D 4e: Each class was given a hybrid-version, which amounted to half the original class options. Mix and match any two classes to create something unique with alternating powers. Some options worked better others, obviously. But it was a fun idea that was still balanced because they shared the same progression as every other class. That was part of the beauty (or dismay, depending on your perspective) of that system. Of course, it might not work so easily with other edition because 4e was designed so radically different.
AD&D (1e & 2e): This was just an option for non-human races who could select more than one class and operate simultaneously (i.e. Fighter/Mage, Mage/Thief, Fighter/Mage/Thief, etc). The down sides were a) some abilities would be cancelled by certain restrictions (i.e. arcane spell-casters had a chance of spell failure for wearing armor, backstabbing only worked with certain weapons, etc.), b) level progression was much slower because your XP would be divided for each class even after c) you could only reach a certain level of each class based on your race and relevant attribute score. Thus, a dwarf Fighter/Cleric might only be allowed to reach level 8 in Cleric (don't quote me, I'm not looking that up) but continue to level 12 in Fighter. His XP would still be divided for both classes even though he cannot gain more Cleric levels.
Pathfinder: The Advanced Class Guide introduced new character classes based on specific class combinations, such as the Arcanist (wizard/sorceror), the Hunter (druid/ranger), and the Inquisitor (rogue/alchemist). But they didn't just mash two classes together and spread out the same abilities or features. They came up with new abilities and features to give each class a unique feel and role to the game.
In a sense, 5e does something similar with specific sub-class options for most classes, such as the Arcane Trickster for Rogues (Mage), and the Eldritch Knight for Fighters (Mage, again). Maybe some more options like this would solve the dilemma, whatever it is.
