Right now my approach is that most things that belong to anyone in the family may belong to one person, but families share things. After all, that is "dad's chair" at the dinning room table but we can all use it if we want. That is "mom's colored pencils" but we can all color with them. And those are "Sofia's toys" but we can all take turns. There are a few things that each person has the final say over (mom's jewelry box, dad's pocket knife, and some special toys), but most things are shared.
Yeah right.
If anyone has any good suggestions or better approaches, please let me know.