The phrase "to extend a family" means to make a family bigger by welcoming new members, such as having children or adopting. It refers to the act of growing and expanding the size of a family unit. Full definition
Perhaps part of the required culture shift is to break down the walls of the western idea of nuclear families and start strengthening the role of extended family members in nurturing family wellness. (slaw.ca)
Help fathers understand and improve their relationships with extended family members. (fatherhood.gov)
In fact, an estimated one out of 11 kids will live with extended family for at least three consecutive months at some point before age 18. (datacenter.kidscount.org)