stepfamily
patchwork family , also: bonus family , also: blended family AmE

Many mothers seek out each other on the registry, eager to create a patchwork family for themselves and their children.

Custo Dalmau is father to 3 daughters (one of which is not his biological daughter) and two sons in a patchwork family.

Bharati Mukherjee: Jasmine (Indian immigrant ends up as the mother in a patchwork family)

Nobody would guess that Sean, Esther, Zachary, Zelda and Kate - Sean's 19 year-old daughter by his first wife, who died of cancer - are a patchwork family.

In this context, the novel's magical realism makes sense: the characters' illnesses (cancer, suicide attempt, etc.) can be regarded, in a figurative way, as "cultural illnesses" that are overcome in the end of the novel, when Kerewin, Joe and Simon form a sort of "patchwork family".

The real Leopold and Agnes did settle here with their patchwork family - eventually there were 18 children in all - and made their home and religious center in Klosterneuburg (Kloster, or "monastery," and Neuburg, or "new castle") on what was actually a former Roman fortress.