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I don’t know about partitives, but I’ve read that there are 2 main types of classifier, one being for countable things and the other for non-countable things. English uses classifiers for non-countable things in much the same way as Thai . For example, water is non-countable, so the phrase “‘three water” is meaningless. It needs a classifier such as glass, bottle, jug, barrel to be added.
Unlike English , Thai also uses classifiers for countable items, such as chairs and dogs, so in Thai we can’t say “three dogs”, we have to say “dog three body”. There are rare exceptions in English - a pedant might say that “‘three cattle” is grammatically incorrect, it should be “three head of cattle”, where “‘head” is the same as a Thai classifier for a countable thing.