Inclusion Criteria:

          -  Postmenopausal women with estrogen receptor positive (ER+), human epidermal growth
             factor receptor 2 (HER2) negative metastatic breast cancer (MBC) who have progressed
             on combination therapy with an aromatase inhibitor and cyclin-dependent kinase 4/6
             (CDK 4/6) inhibitor

               -  Note: Postmenopausal females are considered of childbearing potential unless they
                  are surgically or permanently sterile (have undergone a hysterectomy, bilateral
                  tubal ligation, or bilateral oophorectomy) or they are naturally postmenopausal
                  for at least 12 consecutive months. A high follicle stimulating hormone (FSH)
                  level in the postmenopausal range may be used to confirm a post-menopausal state
                  in women not using hormonal contraception or hormonal replacement therapy.
                  Documentation of postmenopausal status must be provided

          -  Measurable disease per Response Evaluation Criteria in Solid Tumors version 1.1
             (RECIST1.1)

          -  Patients must have had tumor sequencing for evaluation of actionable PIK3CA or PTEN
             mutations performed in a Clinical Laboratory Improvement Act (CLIA) certified, College
             of American Pathologist (CAP) tested and bioinformatics-validated testing lab PRIOR to
             enrollment in this current protocol. If available patient tumor sequencing status must
             be provided to University of North Carolina (UNC) principal investigator (PI) at
             consent, and prior to any additional screening procedures. The testing may have been
             done at any time prior to enrollment. For patients who have not yet had tumor genomic
             assessment, after consultation with the PI, tumor specimens will be sent to the UNC
             Hospitals Clinical Molecular Genetics Laboratory for assessment of the Solid Tumor
             Mutation Panel. In this case, results of genetic testing by the UNC lab must be
             available prior to the first on study disease assessment (i.e., prior to day 1 of
             cycle 4). In this case, the study will cover the cost of the Solid Tumor Panel

          -  Female subjects who are not of childbearing potential

               -  Note: Because no dosing or adverse event data are currently available on the use
                  of copanlisib in combination with fulvestrant in patients <18 years of age, and
                  only postmenopausal women with ER+/HER2 negative MBC are eligible or appropriate
                  for treatment with fulvestrant, children and pregnant or pre-menopausal women are
                  excluded from this study

          -  Eastern Cooperative Oncology Group (ECOG) performance status =< 2 (Karnofsky >= 60%)

          -  No prior treatment history with fulvestrant or a PI3K inhibitor

          -  Subject has not received more than 2 prior lines of chemotherapy in the metastatic
             setting

          -  Subject must have washout period from prior systemic anti-cancer therapy of at least
             21 days (or 5 half-lives of the systemic anti-cancer therapy, whichever is shorter)
             before the start of study treatment

          -  Subject must have washout period from prior radiation therapy of at least 2 weeks
             before the start of study treatment

          -  Subjects with a history of brain metastases are allowed if they are not on steroid
             therapy and there is no evidence of intracranial disease progression symptomatically
             or by imaging within 28 days prior to study registration

          -  Hemoglobin >= 9.0 g/dL (collected no more than 7 days before starting treatment)

          -  Leukocytes >= 3,000/mcL (collected no more than 7 days before starting treatment)

          -  Absolute neutrophil count >= 1,500/mcL (collected no more than 7 days before starting
             treatment)

          -  Platelets >= 100,000/mcL (collected no more than 7 days before starting treatment)

          -  Total bilirubin =< 1.5 x upper limit of normal (ULN) (collected no more than 7 days
             before starting treatment) (< 3 x ULN for patients with Gilbert syndrome, patients
             with cholestasis due to compressive adenopathies of the hepatic hilum or documented
             liver involvement)

          -  Aspartate aminotransferase (AST)(serum glutamic-oxaloacetic transaminase
             [SGOT])/alanine aminotransferase (ALT)(serum glutamate pyruvate transaminase [SGPT])
             =< 2.5 x institutional upper limit of normal (ULN) OR =< 5 x institutional ULN if
             liver metastases present (collected no more than 7 days before starting treatment)

          -  Glomerular filtration rate (GFR) >= 60 mL/min/1.73 m^2 unless data exists supporting
             safe use at lower kidney function values, no lower than 30 mL/min/1.73 m^2 (collected
             no more than 7 days before starting treatment)

          -  Fasting blood glucose < 120 mg/dL (collected no more than 7 days before starting
             treatment)

          -  Lipase =< 1.5 x ULN (collected no more than 7 days before starting treatment)

          -  International normalized ratio (INR) and partial thromboplastin time (PTT) =< 1.5 x
             ULN (collected no more than 7 days before starting treatment)

          -  Left ventricular ejection fraction (LVEF) >= 50%

          -  Subject must agree to provide archival tumor material for research and/or agree to
             undergo a tumor biopsy for research if the tumor is accessible for biopsy prior to
             study treatment

          -  Ability to understand and the willingness to comply with study procedures and to sign
             a written informed consent document

          -  Patients with a prior or concurrent malignancy whose natural history or treatment does
             not have the potential to interfere with the safety or efficacy assessment of the
             investigational regimen are eligible for this trial

        Exclusion Criteria:

          -  Previous assignment to treatment during this study. Patients permanently withdrawn
             from study participation will not be allowed to re-enter the study

          -  Concomitant participation in another clinical study with investigational medicinal
             product

          -  Subjects who have not recovered from adverse events due to prior anti-cancer therapy
             (i.e., have residual toxicities > grade 1) with the exception of alopecia

          -  Immunosuppressive therapy is not allowed while on study

          -  Subjects who are receiving any other investigational agents

          -  History of allergic reactions attributed to compounds of similar chemical or biologic
             composition to copanlisib, fulvestrant, or PI3K inhibitors

          -  Subjects with moderate or severe hepatic impairment (ie, Child-Pugh B or C)

          -  Copanlisib is primarily metabolized by CYP3A4. Therefore, the concomitant use of
             strong inhibitors of CYP3A4 (e.g., ketoconazole, itraconazole, clarithromycin,
             ritonavir, indinavir, nelfinavir and saquinavir), and strong inducers of CYP3A4 (e.g.
             rifampin, phenytoin, carbamazepine, phenobarbital, St. John's Wort) are not permitted
             from 14 days prior to enrollment until the end of the study. Other medications that
             are prohibited while on copanlisib treatment:

               -  Herbal medications/preparations (except for vitamins)

               -  Anti-arrhythmic therapy other than beta blockers or digoxin

          -  Systemic corticosteroid therapy at a daily dose higher than 15 mg prednisone or
             equivalent is not permitted while on study. Previous corticosteroid therapy must be
             stopped or reduced to the allowed dose at least 7 days prior to the computed
             tomography (CT)/magnetic resonance imaging (MRI) screening; if a patient is on chronic
             corticosteroid therapy, corticosteroids should be de-escalated to the maximum allowed
             dose before the screening; patients may be using topical or inhaled corticosteroids;
             short-term (up to 7 days) systemic corticosteroids above 15 mg prednisolone or
             equivalent will be allowed for the management of acute conditions (e.g., treatment
             non-infectious pneumonitis); the use of corticosteroids as antiemetics prior to
             copanlisib administration will not be allowed

          -  Uncontrolled intercurrent illness, including but not limited to, psychiatric
             illness/social situations that would limit compliance with study requirements

          -  Major surgical procedure or significant traumatic injury (as judged by the
             investigator) within 28 days prior to start of treatment, or not recovered from major
             side effects, or open biopsy within 7 days before start of study treatment

          -  Patients with non-healing wound, ulcer, or bone fracture not due to breast cancer

          -  Patients with active, clinically serious infections > grade 2 (Common Terminology
             Criteria for Adverse Events [CTCAE] version [v]5.0)

          -  Patients with glycosylated hemoglobin (HbA1c) > 8.5% at screening

          -  Proteinuria of >= CTCAE grade 3 as assessed by a 24 hour (h) protein quantification or
             estimated by urine protein: creatinine ratio > 3.5 on a random urine sample

          -  Arterial or venous thrombotic or embolic events such as cerebrovascular accident
             (including transient ischemic attacks), deep vein thrombosis or pulmonary embolism
             within 3 months before the start of study medication

          -  Congestive heart failure > New York Heart Association (NYHA) class 2

               -  Note: Class III NYHA Heart failure classification: Patients with cardiac disease
                  resulting in marked limitation of physical activity. They are comfortable at
                  rest. Less than ordinary activity causes fatigue, palpitation, dyspnea, or
                  anginal pain

               -  Note: Class IV NYHA Heart failure classification: Patients with cardiac disease
                  resulting in the inability to carry on any physical activity without discomfort.
                  Symptoms of heart failure or the anginal syndrome may be present even at rest. If
                  any physical activity is undertaken, discomfort is increased.

        Other cardiovascular-related abnormalities or therapy that prohibit study participation
        are:

          -  Myocardial infarction less than 6 months before start of study medications

          -  Unstable angina (angina symptoms at rest), new onset angina (begun within the last 3
             months)

          -  Uncontrolled arterial hypertension despite optimal medical management

          -  Anti-arrhythmic therapy (exceptions: beta blockers or digoxin are permitted)

               -  Pregnant or lactating (Pregnant women or women who are breastfeeding are excluded
                  from this study because copanlisib is a PI3K inhibitor agent with the potential
                  for teratogenic or abortifacient effects; there is no safety data in pregnancy;
                  because there is an unknown but potential risk for adverse events in nursing
                  infants secondary to treatment of the mother with copanlisib, breastfeeding
                  should be discontinued if the mother is treated with copanlisib and/or
                  fulvestrant; fulvestrant may also cause fetal harm and based on animal studies,
                  may impair fertility in females of reproductive potential)

               -  Hepatitis B virus (HBV) or hepatitis C virus (HCV). All patients must be screened
                  for HBV and HCV up to 28 days prior to study drug start using the routine
                  hepatitis virus lab panel; patients positive for hepatitis B virus surface
                  antigen (HBsAg) and/or hepatitis B virus core antibody (HBcAb) will be eligible
                  if they are negative for deoxyribonucleic acid (DNA), these patients should
                  receive prophylactic antiviral therapy; patients positive for anti-HCV antibody
                  will be eligible if they are negative for HCV ribonucleic acid (RNA)

               -  Human immunodeficiency virus (HIV)-positive patients on combination
                  antiretroviral agents that are strong CYP3A4 inhibitors or inducers and who are
                  unwilling or unable to change to antiretroviral therapies without such
                  interactions are ineligible because of the potential for pharmacokinetic
                  interactions with copanlisib

               -  Subjects with seizure disorder requiring medication

               -  Subjects with evidence or history of bleeding diathesis; any hemorrhage or
                  bleeding event >= CTCAE grade 3 within 4 weeks prior to the start of study
                  medication

               -  Blood or platelet transfusion less than 7 days before start of study treatment or
                  myeloid growth factors within 14 days prior to treatment

               -  History of concurrent condition of interstitial lung disease of any severity
                  and/or severely impaired lung function (as judged by the investigator)

               -  History of, or current autoimmune disease

               -  Concurrent diagnosis of pheochromocytoma