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. They get some information about Tibet and will probably get much more [information]when they send more experienced reporters to cover the situation.
'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: