Consider a hypothetical polygamous patriarchal society in which the men take multiple wives. Somewhat analogously, the women, while permitted only one husband, take multiple additional lovers. Critically, however, the children produced of a wife and lover belong to the family of the wife and husband, not the biological father. This kind of "adultery" is not frowned upon but instead encouraged: the wives are expected to use their intellect and instinct to select and mate with the men most fit for the environment in hopes of producing the fittest offspring for the continuation of the patriarchal family.
The society believes that nurture trumps nature. The children in the family are inculcated with the behaviors, values, culture, and trust relationships of and toward the family and patriarch, not the biological father.
Can such a society exist? (Does it exist? Has it existed?) Or does the biological imperative of "my sperm must propagate" inevitably cause the patriarch to limit the sexual freedom of his wives?