Several autoimmune diseases such as Addison's disease are associated with failing ovarian function, known as premature ovarian insufficiency (POI), which can lead to early menopause and reduced fertility.The underlying cause of POI in these women is considered to be an immunological attack on the ovaries that causes them to not respond to hormonal stimulation from the brain. Hormone replacement effectively counteracts menopausal symptoms, but today there is no treatment to normalize or even improve fertility. As a patient with POI and an autoimmune diagnosis and the desire to become pregnant, you are asked to participate in the study. The aim of this study is to investigate whether immunomodulatory therapy can improve and ideally normalize ovarian function in women of childbearing age with autoimmune disease and proven POI. Patients with a male partner and a desire for children and who respond positively to the first ovarian stimulation will be offered in vitro fertilization (IVF) and will thus be allowed to complete the study. Other participating patients will undergo a total of three ovarian stimulations and treatment with first two infusions of the registered drug rituximab or placebo (inactive agent) and later two additional infusions where all patients receive rituximab. The first two infusions with rituximab or placebo are double-blind, which means that neither you nor the study staff know what you have received. Follow-up takes place up to 12 months after the last infusion.