Note that "more" can be either an adjective or an adverb, depending on how it's used. Also note that an adverb can either precede or follow a verb:
They quickly drove to the store
They drove quickly to the store
Although it's probably not good style, an adverb can commonly appear far away from the verb:
They drove to the store quickly.
So in your examples, even though "some more" appears before a noun, it's not immediately clear whether it modifies the verb, or the following noun.
Would you like some more cake?
How much do you want?" Some more. Or, "How much cake do you want?" Some more.
If the rice is still not cooked, add some more water.
"How much do I add?" Some more. Or, "How much water do I add?" Some more.
I need to work on it some more.
"How much do you need to work?" Some more. Or, "How much do you need to work on it? Some more.
Either way works. It just depends on what part of the sentence you choose to emphasize.
Ultimately, remember that labeling parts of speech, in any language, is only an artificial exercise designed to help with comprehension. What's more important is how well you can communicate in that language.