One example are the words much and many. Both of them basically mean “a lot,” but much goes with amorphous masses and many goes with individual countable items. So if you say “much wine was consumed,” you’re talking about a large sea of wine, but if you say “many wines were consumed,” you’re talking about many individual wine-items, in this case probably types of wine like Pinot Grigio or Merlot. But some combinations are better than others: “many wine” or “much wines” is definitely not in the canon of Standard English, but sounds excellent in doge speak.
An example that proves my point conveniently popped up on my Facebook while I was writing this, showing someone actually correcting someone else’s use of doge modifiers to be more ungrammatical.
Friend #1 (posting link): Doge is a rescue dog. Much respect. So noble. Wow.
Friend #2 (commenting): Your dogeing is too coherent. “Much noble, so respect.”
So it would be “much noun”, because nouns are countable items. “Many noun” is still ungrammatical, and pretty much still acceptable, as the plural/singular doesn’t match up, but not precisely correct.