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A closed group marriage is a polyfidelitous marriage consisting of three or more people. The participants in a closed group marriage agree not to have partners outside the marriage, but new partners may be added to the group if all members agree. While the participants in a closed group marriage do not practice monogamy, they do practice fidelity.
Closed group marriages are a good example of the distinction between monogamy and fidelity. While a closed group marriage involves multiple partners and thus its participants are not monogamous, it also features an agreement to not engage with individuals outside the marriage, requiring the participants to practice fidelity.