Yes, 'many more.' We use 'many' instead of 'much' in this case because we are talking about 'schools,' even though the word 'schools' does not appear.

'Schools' is a plural count noun, and thus is modified by 'many,' not by 'much.'

If a noncount noun were being used, a noun like information, for example, we'd use 'more' in a sentence like this:

  • They get some information about Tibet and will probably get much more [information]when they send more experienced reporters to cover the situation.
  • One of my grammar books lists some adverbs that can modify a comparative adjective like much, far, a lot.
    (a) I have a lot more friends.
    (b) I have far more friends.
    (c) I have much more friends.

    I presume there is no problem with (a) and (b).
    But (c) is incorrect?
    The examples are from me not from a grammar book.
    Anyway, I understand you mean much more + countable noun is incorrect.
    But in fact, I can find so many expressions such as much more books, cars, etc on the internet, even on Google books or news sites.
    In particular, I can see the expression of "much more people" is widely used. This fact makes me embarrassed.

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