No, in His dog, cat and crocodile are three happinesses of his life, happiness is countable. What I said is that many nouns can be both uncountable and countable (and in the latter case can of course assume both singular and plural forms). The acceptability of either form (in whatever register or medium) is dependent on the appropriacy of the usage.
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MilkyI hate the use "happinesses". Sounds horrible. Use "joys" there.Same feeling here.