The following examples are clearly wrong:
× I am very much tired
× She is very much clever
But the following sounds fine (at least according to OALD):
I am very much afraid that ...
I am very much aware of ...
Worse, the following sounds awkward to me:
× I am very aware of ...
I wonder some sound ok while the others do not. Does it have to do with the type of adjectives being used? Or is there a subtle nuance between "very" and "very much"? Is "very much" the same as "extremely" (I would guess not, at least in the "afraid" example)? When should/can one use "very much", as opposed to "very"? Are there differences between spoken and written uses?