Um, normal mode is normal attack (Rebellion) Light mode is light attack (Osiris) Heavy mode is heavy attack (Arbiter).
All you would have managed to do is turn it into an unnecessary mess that lowers the amount of moves possible, and makes it more difficult to handle.
First of all, Normal Mode is Normal Mode, it incorporates its only style of combat unique to the others, so it's more than just an attack type.
Now what I'm saying is instead of having modes to access different attacks, you can put all the attacks onto a single button with different inputs. Same thing with special moves and movements. It's not that complicated, Bayonetta pulled it off by having gun and punch/kick attacks all on the same button, and plenty of games have had different attacks such as light and heavy attacks on the same button as well with heavy attacks being the same as charged attacks. A game like DmC can benefit from that since it promises efficiency, hand freedom, and allow greater attack variety.
Here, I'll use different examples:
Normal Dodge---> X + D-pad
Angel Dodge/Dash---> D-Pad + X, (immediately)X
Demon Ram---> (hold) X + D-Pad
Angel Grab---> Up + O
Demon Grab---> Down + O
Normal Grab---> O (O (again) + D-Pad, for swings/throws or alternative grab attacks)
You see where I'm getting at now? If you were allowed to make up extensive combos, here's how one would like:
Triangle, Triangle, (pause) Triangle, Triangle, Triangle, (hold)R1 + Down + Triangle, (pause) Triangle, (hold) Triangle
Translation: Normal, Normal, Angel, Normal, Normal, Demon Launcher, Angel, Demon
All that with just the Triangle button, here's with Grabs:
Triangle, (hold) Triangle, Down + O, Triangle, (pause) Triangle, Triangle, Triangle, Triangle
Translation: Normal, Demon, Demon Grab, Normal, Angel, Normal, Normal, Normal.
Now if you guys don't get it up to this point, I would be forced to pull up the dreaded Youtube.