Maybe instead of a binary stagger bar (where you are either CCed or not), how about CCs having two phases.
One effect while filling the stagger bar, and another when full.
Like Stun:
If hit once by a stun, maybe your stagger bar fills 50% (this depends on the power of the monster applying it). You are not stunned, but are slowed and your ability cost increased by 50% (got to think harder to pull off your abilities due to the concussion. Lolrealism™!).
You get hit by another stun and the stagger goes to 75% or whatever. Slowed and 75% increased resource cost. Then another hit and you pass 100% and are now actually stunned.
Stagger goes down over time of course - and might be affected by skills, gear etc.
That way, even if the strong CC effects do not happen particularly often, and thus not breaking down the combat flow constantly), the soft effects might happen fairly regularly, and force you to be more careful to avoid the hard CC.
To make those soft CC effects more interesting for gameplay, let them have some more effect than the usual “you are slowed”.
Another could be like the players chill effect.
First chill slows you, and makes your skills take a bit more time to cast. If staggered, you are frozen.
Poison: If at 50% poison stagger, your heal effects are reduced by 25%. If 100%+ poison stagger you get a 10 sec debuff on you, that deals dmg to you, the more you move around.
Fire: If at 50% fire things are heating up; your ressource regeneration is reduced by 25%. if above 100% fire stagger, you are burning. A 10 sec debuff is applied, dealing more dmg the less you are moving.
(or whatever, just examples for the sake of if)
Now, there should not be a stagger bar for every single CC effect, as that would likely be too much information to digest in the middle of combat.
So if you are hit by a stun effect and then a freeze effect, only the strongest effect is applied. Like your stun stagger is at 10%, a 20% freeze hits you and the stagger changes to a 20% freeze stagger. If your stun stagger was at 80%, nothing happens. You might even try to use that to your advantage in combat.
Color code our stagger bar so we can easily see which CC effect is currently applied. Like Brown = stun, blue = freeze, purple = feared, etc.