Copanlisib in Combination With T-DM1 in Pretreated Unresectable Locally Advanced or Metastatic HER2-positive Breast Cancer

This study is a phase Ib open label, single arm, adaptive multi-centre trial. Patients with unresectable locally advanced or metastatic HER2-positive breast cancer who previously received trastuzumab and a taxane, separately or in combination, will be treated with copanlisib plus trastuzumab emtansine 3.6mg/kg IV on day 1 of a 21-day cycle. 3 to 6 patients will be enrolled per dose level. All patients in each level must have completed at least the first cycle of therapy before enrolment in the next dose level begins. Patients not completing the first cycle for a reason other than toxicity will be replaced. Copanlisib will start at a low level and dose escalations will be performed in cohorts of 3 patients according to a standard 3+3 algorithm. Dose escalation and determination of maximum tolerated dose (MTD) will be based on occurrences of Dose Limiting Toxicities (DLT). The first cohort of 3 patients will commence at dose level 1. All patients in each cohort will be observed for one cycle on the specified dose: * If none of 3 patients at a given dose level experiences a DLT, accrual will continue to the next dose level according to the protocol. * If 1 of 3 patients experiences a DLT at a given dose level, 3 additional patients will be treated at the same dose. If no additional patient has a DLT in this cohort, accrual will continue to the next dose level according to the protocol. * If 2 or more patients in 3 or 6 patients treated at a given dose experience a DLT, the dose will be de-escalated to the next lower dose level, which will define the MTD. If 2 or more patients in 3 or 6 patients treated at the -1 dose level experience DLT, the trial will be stopped. Primary Objective: 1\. To determine the Maximum Tolerated Dose (MTD), for copanlisib in combination with trastuzumab emtansine (T-DM1) in patients with pretreated unresectable locally advanced or metastatic HER2-positive breast cancer. Secondary Objectives: 1. To evaluate the safety and tolerability of this regimen. 2. To evaluate efficacy measures in patients treated with this regimen. 3. To assess the incidence of cardiotoxicity in patients treated with this regimen. Exploratory Objectives: 1. To examine for predictive biomarkers in tumour tissue and blood. 2. To examine molecular tumour adaptation to clinical trial therapy.