Testing the Addition of an Anti-cancer Drug, Copanlisib, to the Usual Maintenance Treatment (Trastuzumab and Pertuzumab) After Initial Chemotherapy in a Phase Ib/II Trial for Advanced HER2 Positive Breast Cancer

Inclusion Criteria:

* Phase 1B: Any prior number of lines of therapy in metastatic setting is allowed, provided patients are considered candidates for trastuzumab and pertuzumab combination or on maintenance trastuzumab and pertuzumab (with or without prior chemotherapy) as long as dose limiting toxicity (DLT) can be determined. For Phase 2:Patients should have only received first line of induction chemotherapy (taxane) with trastuzumab and pertuzumab in the metastatic setting
* Presence of actionable mutation in either PIK3CA or PTEN on molecular testing
* For Phase 2-Patients must be within 8 weeks of completion of first-line induction chemotherapy (i.e., 4-8 cycles of any taxane, trastuzumab and pertuzumab) without evidence of progression. Patients may receive up to 2 doses of HER2 targeted treatment between end of induction treatment and start of trial, while eligibility is being confirmed
* Clinical stage IV as assessed by American Joint Committee on Cancer (AJCC) (8th edition, anatomic staging) guidelines with known metastatic disease (Edge and Compton, 2010; Amin et al., 2017)
* HER2+ breast cancer patients with any ER/PR status as assessed by the American Society of Clinical Oncology (ASCO)-College of American Pathologists (ASCO-CAP) guidelines (Wolff et al., 2013; Wolff et al., 2018). HER2 testing of metastasis will be required
* Eastern Cooperative Oncology Group (ECOG) performance status =\< 2 (Karnofsky \>= 50%)
* Absolute neutrophil count (ANC) \>= 1,500/mcL
* Platelets \>= 100,000/mcL
* Hemoglobin \>= 9 g/dL
* Left ventricular ejection fraction (LVEF) \>= 50% by echocardiogram or multigated acquisition scan (MUGA)
* Total bilirubin =\< 1.5 x institutional upper limit of normal (ULN) OR direct bilirubin =\< ULN for subjects with total bilirubin levels \> 1.5 x ULN
* Aspartate aminotransferase (AST) (serum glutamic-oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 2.5 x institutional ULN OR =\< 5 x ULN for subjects with liver metastases
* Creatinine =\< 1.5 x institutional ULN OR measured or calculated creatinine clearance \>= 60 mL/min for subject with creatinine levels \> 1.5 x institutional ULN (glomerular filtration rate \[GFR\] can also be used in place of creatinine or creatinine clearance \[CrCl\]). Creatinine clearance should be calculated per institutional standard
* International normalized ratio (INR) OR prothrombin time (PT) =\< 1.5 x ULN unless patient is receiving anticoagulation as long as PT or partial thromboplastin time (PTT) is within therapeutic range of intended use of anticoagulants
* Activated partial thromboplastin time (aPTT) =\< 1.5 x ULN unless patient is receiving anticoagulation as long as PT or PTT is within therapeutic range of intended use of anticoagulants
* Patients with treated brain metastases are eligible if follow-up brain imaging 30 days after central nervous system (CNS)-directed therapy shows no evidence of progression
* Patients who are therapeutically treated with anticoagulation including warfarin will be allowed to participate provided that their medication dose and INR/PTT is stable. Due to interaction of copanlisib with warfarin, patients who are on warfarin should be monitored closely while on this trial
* Women of child-bearing potential MUST have a negative serum or urine human chorionic gonadotropin (HCG) test unless prior tubal ligation (\>= 1 year before screening), total hysterectomy or menopause (defined as 12 consecutive months of amenorrhea). Patients should not become pregnant or breastfeed while on this study
* Patients and their partners, if sexually active and of childbearing potential, must agree to the use of two highly effective forms of contraception in combination throughout the period of taking study treatment and for 7 months after last dose of study drug(s) to prevent pregnancy in the study patient or partner
* Hormone receptor positive (ER+ and / PR+) breast cancer patients will be allowed to continue endocrine therapy as clinically indicated while participating in the study.
* Ability to understand and the willingness to sign a written informed consent document

Exclusion Criteria:

* Known active hepatitis B or hepatitis C infection. All patients must be screened for hepatitis B virus (HBV) and hepatitis C virus (HCV) up to 28 days prior to study drug start using the routine hepatitis virus lab panel. For patients with evidence of chronic hepatitis B virus (HBV) infection, the HBV viral load must be undetectable on non-CYP3A4-interactive suppressive therapy, if indicated. Patients with a history of hepatitis C virus (HCV) infection must have been treated and cured. Patients positive for anti-HCV antibody will be eligible if they are negative for HCV ribonucleic acid (RNA)
* Human immunodeficiency virus (HIV)-positive patients, unless they have CD4 counts \> 500 cells/mm\^3 in the past 6 months and do not require CYP3A4-interactive antiretroviral therapy
* Active infection requiring IV antibiotics or other uncontrolled intercurrent illness requiring hospitalization
* Inability to comply with the study and follow-up procedures
* History of cerebrovascular accident (CVA), myocardial infarction, symptomatic congestive heart failure, cardiac arrhythmia, or unstable angina within the previous 6 months before starting therapy
* Patients who have not recovered from adverse events due to prior anti-cancer therapy (i.e., have residual toxicities \> grade 1) with the following exceptions: alopecia (any grade is acceptable); neuropathy must have resolved to =\< grade 2. Congestive heart failure (CHF) due to prior anti-cancer therapy must have been =\< grade 1 in severity at the time of occurrence, and must have resolved completely
* Current uncontrolled hypertension (\>= 150/90)
* Has a known additional malignancy that is progressing or requires active treatment. Exceptions include basal cell carcinoma of the skin, squamous cell carcinoma of the skin that has undergone potentially curative therapy or in situ cervical cancer
* Has a known psychiatric or substance abuse disorders that would interfere with cooperation with the requirements of the trial
* Patients with uncontrolled type I or II diabetes mellitus (DM); uncontrolled DM is defined as glycosylated hemoglobin (HbA1c) \> 8.5% and a fasting blood glucose of \> 120 mg/dL within 14 days prior to trial entry
* Immunosuppressive therapy is not allowed while on study
* Patients who are receiving any other investigational agents
* Patients with leptomeningeal disease or active untreated brain metastases
* Prior exposure to any PI3K, AKT or mTOR inhibitors. History of allergic reactions attributed to compounds of similar chemical or biologic composition to copanlisib, PI3K inhibitors, or HER2 inhibitors
* 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
  * Because the lists of these agents are constantly changing, it is important to regularly consult a frequently-updated medical reference for a list of drugs to avoid or minimize use of. As part of the enrollment/informed consent procedures, the patient will be counseled on the risk of interactions with other agents, and what to do if new medications need to be prescribed or if the patient is considering a new over-the-counter medicine or herbal product
* 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
* Patients with non-healing wound, ulcer, or bone fracture
* Pregnant women are excluded from this study because copanlisib is a PI3K inhibitor agent with the potential for teratogenic or abortifacient effects. 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. These potential risks may also apply to other agents used in this study
* Patients are eligible to receive standard of care therapy that would confer clinical benefit to the patient