WikiTree allows records for multiple spouses so you can create a second spouse for your father, for instance, and add their children on her profile, making sure your father is listed as your half siblings' father. When you click on your father's profile, all his children will show up as siblings. When you click on individual spouses' profiles, it will show only the children they had with your father.
For situations of adoption, create profiles for the adoptive parents then add a link in your brother's biography to the adoptive parents. On WikiTree, genetic parents should be listed as the primary parents because genealogy deals with blood lines and we have DNA information going up and down the family lines. DNA information going through an adoptive line wouldn't be accurate. Adoptive parents are very important so they can still be included through links within the biography.