Being embedded in social networks is crucial for well-being and health. While this is particularly the case for people with Down syndrome (DS), our knowledge of how their support networks are developed is limited. This article investigates the role of family members in developing and maintaining the social support networks of their adult children with DS. Based on 29 interviews with family members, a grounded theory study was conducted. The Family Building and Connecting (BAC) framework was developed, which distinguishes a “building” and a “connecting” approach. The building approach includes strategies that rely on family members and close friends for building a support network for the person with DS. The connecting approach includes strategies that connect the person with DS to external and often professional resources and services. Distinguishing these approaches is important for future research and for strengthening the support networks of people with DS and their families.