After going through various suggestions by GMAT experts at
Magoosh and Manhattan, I could arrive at the following conclusion:
The positive....comparative...superlative forms of certain adjectives of quantity are as follows:
set 1. many...more...most
set 2. much...more....most
set 3. great...greater...greatest
While set 1 (many...more...most) is used for countable nouns, set 2 (much...more....most) and set 3 (great...greater...greatest) are used for uncountable nouns.
Now there could be 2 types of uncountable nouns
type a. Quantity word / numbers themselves (e.g. price, volume, weight, probability etc.) are uncountable.
type b. Other uncountable nouns (honesty, poverty, etc as you mentioned)
The set 2 (much...more....most) is used for type b (other uncountable nouns) uncountable nouns.
The set 3 ( great...greater...greatest) is used for type a (Quantity word / numbers) uncountable nouns.
Therefore we see that "more" can be used for (i) countable nouns and (ii) uncountable nouns that are not quantity words/ numbers.
"Greater" can be used for (iii) uncountable nouns that are quantity words/ numbers.
What about high? High Higher Highest vs Great Greater Greatest . Eg: Higher probability of something happening vs Greater Probability happening. How would look at that.