The best replacement for possessive pronouns is possessive adjectives.

The best alternatives to possessive pronouns are rated as following:
★★★★★  possessive adjectives
★★★★★  contractions
★★★  personal pronouns
★★★  adjectives
★★  possessive nouns
★  possessive adjective
★  adjectives exercises
  determiners

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Speaking about possessive pronouns, one probably shouldn't forget about gerunds.

Other search terms related to possessive pronouns and their ratings are:
★★★★★ gerunds
★ apostrophe
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possessive pronouns
possessive adjectives
contractions