I don't think including for would ever affect the meaning. Since continuing to run is a relatively uncommon activity, let's look at...
slept longer than (46,500 hits in Google Books)
slept for longer than (979 hits)
I can't say I think there's anything wrong with #2 there, but it's worth noting that you can't introduce for with other "comparative adverbs". It's okay with longer, but ...
- "I ran for faster than you, so I finished first" (not valid English)
So given that for longer isn't particularly common anyway, and it doesn't involve a principle which can be extrapolated to other contexts, I'd say it's not really worth learning (except if you need to satisfy yourself that the usage isn't actually "incorrect").
No. These sentences use two different senses of the word very.
He is the very image of sophistication.
This sentence uses an older sense of the word very. It means true or definitive.
He is the true image of sophistication.
His image defines sophistication, or he defines the image of sophistication.
This sense of very is always used with the definite article. This makes sense because there is nothing more definite than the definitive. This special sense of true always modifies a noun.
This is very much the story of a story.
This sentence uses the common sense of the word very. Here, the word very intensifies the word much. It does not make sense to substitute "true" or "definitive" in this sentence:
This is true much the story of a story. This is definitive much the story of a story.
True modifies the word image in the first sentence. Image is a noun. In the second sentence, very modifies much. The word much is not a noun. This works because the common sense of very does not modify nouns. When the common sense is used, it is not always combined with the definitive article, and the article is not always placed before the word very. For example:
This is very much a story about stories.
In short, you're looking at two different meanings for the word very, and each meaning has its own grammar.
Best Answer
Neither sides is inlined to protract the dispute much longer/any longer/any more
As far as the phrases "any more" and "any longer" are concerned, they are interchangeable, without any difference in meaning.
As for the phrases "much longer" and "any longer/any more", though they can be used in the sentence, they are not interchangeable because they convey different senses.
If you wan to emphasize that neither sides is inclined to protract the dispute even to a small degree/in the least, you can use any more/any longer. On the other hand, the use of "much longer" in the sentence conveys the sense that either of the sides can stand the protraction of the dispute by a small amount/degree, but not to a greater amount/degree.