Patients with HER2 positive, metastatic or incurable recurrent breast cancer, following disease progression during, or after, treatment with at least one systemic treatment regimen in the metastatic or recurrent setting, will be treated with copanlisib (at 30, 45 or 60 mg flat dosing IV weekly - depending on the maximum tolerated dose (MTD) determined in the Phase Ib part of the study) plus trastuzumab (4 mg/kg IV Cycle 1 Day 1 and then 2 mg/kg IV weekly starting from day 8).