I got it working:
Its not necessary to change any material on the plane or the character.
Its only necessary to assign the PostProcessing material in the PostProcessingVolume.
And then remove the masking plane mesh from the main pass:
So basically, this is all thats needed:
Original PostProcessing material:
As it was already ^.
Then all we have to do is:
Disable the actual plane that is masking the mesh from rendering in the Main pass:
Character mesh renders as default, and with original material, and everything defaulty.