Agnès de Viaris, a psychologist specializing in family issues, tells us more
There is no role to play, let alone that of the father or the mother. The step-parent must be himself. He is naturally involved with the child under his roof. It's a matter of adult responsibility that takes a child under his wing. The amalgamations come from the confusion between what relates to the masculine and the feminine of what relates to the father and the mother. A stepfather is not a dad but remains a man in his social function, limits and a form of authority.
Similarly, a mother-in-law is a woman with mothering behavior and is placed in the center of the home. The essential idea is that a child who is under the roof of a parent, step-parent, grandparents, godfather, godmother, educator, adoptive parent ..., is under the responsibility of the adult who must take care of him, guide him and accompany him in his growth and his progress. The amalgam does not have to be with the father or the mother if there is not this sense of confusion of the roles.
Blended Family: Role Of The Step-parent (April 2021)