All species of geese form long-term mated pairs. In the wild, it is usually two birds together for life. In captivity, domestic geese may sometimes be paired with multiple partners to increase fertility, but even these breeder flocks are kept together for life.
Both Canada geese and greylag geese have been well-studied in terms of reproductive behavior. Canada geese form bonds that last for the pair's entire reproductive life, even after fledglings leave the nest. Sometimes a Canada goose takes other partners, but this is only if its mate is injured or lost.
Greylag geese, from which Western domestic geese are derived, also mate for life. Rarely, males take multiple partners. However, the bonds formed with multiple females also last for life. Farmers with geese encourage their birds to form breeding flocks of four to six females for every male and keep all the birds together for as long as they are capable of reproducing.