The best replacement for countif is countifs.

The best alternatives to countif are rated as following:
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★★★★★  criteria
★★★★  statement excel
★★★  sumif
★  multiple criteria
★  counta
★  condition excel
★  sumproduct

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Speaking about countif, one probably shouldn't forget about multiple criteria.

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★ multiple conditions
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or in excel
countif
multiple arguments
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countif
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criteria