Yes, an application for step-adoption is submitted by the stepparent who wants to adopt their stepchild.

If you have been cohabiting or married to a parent of the prospective adopted child for at least five years and have been involved in the parental role and the upbringing of the prospective adopted child, you may apply for step-adoption under certain conditions.

Further information on step-adoptions of individuals over the age of 18 can be found here.